idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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7,801 | What's the point of time series analysis? | Time series analysis can also contribute to effective anomaly or outlier detection in temporal data.
As an example, it is possible to fit an ARIMA model and calculate a forecast interval. Depending on the use case, the interval can be used to set a threshold, within which the process can be said to be in control; if n... | What's the point of time series analysis? | Time series analysis can also contribute to effective anomaly or outlier detection in temporal data.
As an example, it is possible to fit an ARIMA model and calculate a forecast interval. Depending o | What's the point of time series analysis?
Time series analysis can also contribute to effective anomaly or outlier detection in temporal data.
As an example, it is possible to fit an ARIMA model and calculate a forecast interval. Depending on the use case, the interval can be used to set a threshold, within which the ... | What's the point of time series analysis?
Time series analysis can also contribute to effective anomaly or outlier detection in temporal data.
As an example, it is possible to fit an ARIMA model and calculate a forecast interval. Depending o |
7,802 | What's the point of time series analysis? | To add some color to the anomaly detection answer by redhqs, at work I build anomaly detection models for operational metrics like sales and traffic flows. We do the time series analysis to understand what sales ought to be if everything is working as expected, and then compare these to the observed values to see wheth... | What's the point of time series analysis? | To add some color to the anomaly detection answer by redhqs, at work I build anomaly detection models for operational metrics like sales and traffic flows. We do the time series analysis to understand | What's the point of time series analysis?
To add some color to the anomaly detection answer by redhqs, at work I build anomaly detection models for operational metrics like sales and traffic flows. We do the time series analysis to understand what sales ought to be if everything is working as expected, and then compare... | What's the point of time series analysis?
To add some color to the anomaly detection answer by redhqs, at work I build anomaly detection models for operational metrics like sales and traffic flows. We do the time series analysis to understand |
7,803 | What's the point of time series analysis? | There are plenty of other statistical methods, such as regression and
machine learning, that have obvious use cases: regression can provide
information on the relationship between two variables, while machine
learning is great for prediction.
You answer your own question, below: autocorrelation. Time series usua... | What's the point of time series analysis? | There are plenty of other statistical methods, such as regression and
machine learning, that have obvious use cases: regression can provide
information on the relationship between two variables, w | What's the point of time series analysis?
There are plenty of other statistical methods, such as regression and
machine learning, that have obvious use cases: regression can provide
information on the relationship between two variables, while machine
learning is great for prediction.
You answer your own question... | What's the point of time series analysis?
There are plenty of other statistical methods, such as regression and
machine learning, that have obvious use cases: regression can provide
information on the relationship between two variables, w |
7,804 | What's the point of time series analysis? | In addition to the excellent answers provided by others, I would like to comment on how time series analyses are used in electrical engineering.
A large part of electrical engineering consists of modulating voltages and currents to transmit information, or using sensors to convert a physical signal (such as a sound wa... | What's the point of time series analysis? | In addition to the excellent answers provided by others, I would like to comment on how time series analyses are used in electrical engineering.
A large part of electrical engineering consists of mod | What's the point of time series analysis?
In addition to the excellent answers provided by others, I would like to comment on how time series analyses are used in electrical engineering.
A large part of electrical engineering consists of modulating voltages and currents to transmit information, or using sensors to con... | What's the point of time series analysis?
In addition to the excellent answers provided by others, I would like to comment on how time series analyses are used in electrical engineering.
A large part of electrical engineering consists of mod |
7,805 | What is normality? | The assumption of normality is just the supposition that the underlying random variable of interest is distributed normally, or approximately so. Intuitively, normality may be understood as the result of the sum of a large number of independent random events.
More specifically, normal distributions are defined by the ... | What is normality? | The assumption of normality is just the supposition that the underlying random variable of interest is distributed normally, or approximately so. Intuitively, normality may be understood as the resul | What is normality?
The assumption of normality is just the supposition that the underlying random variable of interest is distributed normally, or approximately so. Intuitively, normality may be understood as the result of the sum of a large number of independent random events.
More specifically, normal distributions ... | What is normality?
The assumption of normality is just the supposition that the underlying random variable of interest is distributed normally, or approximately so. Intuitively, normality may be understood as the resul |
7,806 | What is normality? | One note: The assumption of normality is often NOT about your variables, but about the error, which is estimated by the residuals. For example, in linear regression $Y = a + bx + e$; there is no assumption that $Y$ is normally distributed, only that $e$ is. | What is normality? | One note: The assumption of normality is often NOT about your variables, but about the error, which is estimated by the residuals. For example, in linear regression $Y = a + bx + e$; there is no assum | What is normality?
One note: The assumption of normality is often NOT about your variables, but about the error, which is estimated by the residuals. For example, in linear regression $Y = a + bx + e$; there is no assumption that $Y$ is normally distributed, only that $e$ is. | What is normality?
One note: The assumption of normality is often NOT about your variables, but about the error, which is estimated by the residuals. For example, in linear regression $Y = a + bx + e$; there is no assum |
7,807 | What is normality? | A related question can be found here about the normal assumption of the error (or more generally of the data if we do not have prior knowledge about the data).
Basically,
It is mathematically convenient to use normal distribution. (It's related to Least Squares fitting and easy to solve with pseudoinverse)
Due to Cent... | What is normality? | A related question can be found here about the normal assumption of the error (or more generally of the data if we do not have prior knowledge about the data).
Basically,
It is mathematically conveni | What is normality?
A related question can be found here about the normal assumption of the error (or more generally of the data if we do not have prior knowledge about the data).
Basically,
It is mathematically convenient to use normal distribution. (It's related to Least Squares fitting and easy to solve with pseudoi... | What is normality?
A related question can be found here about the normal assumption of the error (or more generally of the data if we do not have prior knowledge about the data).
Basically,
It is mathematically conveni |
7,808 | What is normality? | You can't know whether there normality and that's why you have to make an assumption that's there.
You can only prove the absence of normality with statistic tests.
Even worse, when you work with real world data it's almost certain that there isn't true normality in your data.
That means that your statistical test is a... | What is normality? | You can't know whether there normality and that's why you have to make an assumption that's there.
You can only prove the absence of normality with statistic tests.
Even worse, when you work with real | What is normality?
You can't know whether there normality and that's why you have to make an assumption that's there.
You can only prove the absence of normality with statistic tests.
Even worse, when you work with real world data it's almost certain that there isn't true normality in your data.
That means that your st... | What is normality?
You can't know whether there normality and that's why you have to make an assumption that's there.
You can only prove the absence of normality with statistic tests.
Even worse, when you work with real |
7,809 | What is normality? | The assumption of normality assumes your data is normally distributed (the bell curve, or gaussian distribution). You can check this by plotting the data or checking the measures for kurtosis (how sharp the peak is) and skewdness (?) (if more than half the data is on one side of the peak). | What is normality? | The assumption of normality assumes your data is normally distributed (the bell curve, or gaussian distribution). You can check this by plotting the data or checking the measures for kurtosis (how sha | What is normality?
The assumption of normality assumes your data is normally distributed (the bell curve, or gaussian distribution). You can check this by plotting the data or checking the measures for kurtosis (how sharp the peak is) and skewdness (?) (if more than half the data is on one side of the peak). | What is normality?
The assumption of normality assumes your data is normally distributed (the bell curve, or gaussian distribution). You can check this by plotting the data or checking the measures for kurtosis (how sha |
7,810 | What is normality? | Other answers have covered what is normality and suggested normality test methods. Christian highlighted that in practice perfect normality barely exists.
I highlight that observed deviation from normality does not necessarily mean that methods assuming normality may not be used, and normality test may not be very usef... | What is normality? | Other answers have covered what is normality and suggested normality test methods. Christian highlighted that in practice perfect normality barely exists.
I highlight that observed deviation from norm | What is normality?
Other answers have covered what is normality and suggested normality test methods. Christian highlighted that in practice perfect normality barely exists.
I highlight that observed deviation from normality does not necessarily mean that methods assuming normality may not be used, and normality test m... | What is normality?
Other answers have covered what is normality and suggested normality test methods. Christian highlighted that in practice perfect normality barely exists.
I highlight that observed deviation from norm |
7,811 | What is normality? | To add to the answers above: The "normality assumption" is that, in a model
$Y=\mu+X\beta +\epsilon$,
the residual term $\epsilon$ is normally distributed. This assumption (as in ANOVA) often goes with some other:
2. The variance $\sigma^2$ of $\epsilon$ is constant,
3. independence of the observations.
Of this three a... | What is normality? | To add to the answers above: The "normality assumption" is that, in a model
$Y=\mu+X\beta +\epsilon$,
the residual term $\epsilon$ is normally distributed. This assumption (as in ANOVA) often goes wit | What is normality?
To add to the answers above: The "normality assumption" is that, in a model
$Y=\mu+X\beta +\epsilon$,
the residual term $\epsilon$ is normally distributed. This assumption (as in ANOVA) often goes with some other:
2. The variance $\sigma^2$ of $\epsilon$ is constant,
3. independence of the observatio... | What is normality?
To add to the answers above: The "normality assumption" is that, in a model
$Y=\mu+X\beta +\epsilon$,
the residual term $\epsilon$ is normally distributed. This assumption (as in ANOVA) often goes wit |
7,812 | Generating random variables from a mixture of Normal distributions | In general, one of the easiest ways to sample from a mixture distribution is the following:
Algorithm Steps
1) Generate a random variable $U\sim\text{Uniform}(0,1)$
2) If $U\in\left[\sum_{i=1}^kp_{k},\sum_{i=1}^{k+1}p_{k+1}\right)$ interval, where $p_{k}$ correspond to the the probability of the $k^{th}$ component of t... | Generating random variables from a mixture of Normal distributions | In general, one of the easiest ways to sample from a mixture distribution is the following:
Algorithm Steps
1) Generate a random variable $U\sim\text{Uniform}(0,1)$
2) If $U\in\left[\sum_{i=1}^kp_{k}, | Generating random variables from a mixture of Normal distributions
In general, one of the easiest ways to sample from a mixture distribution is the following:
Algorithm Steps
1) Generate a random variable $U\sim\text{Uniform}(0,1)$
2) If $U\in\left[\sum_{i=1}^kp_{k},\sum_{i=1}^{k+1}p_{k+1}\right)$ interval, where $p_{k... | Generating random variables from a mixture of Normal distributions
In general, one of the easiest ways to sample from a mixture distribution is the following:
Algorithm Steps
1) Generate a random variable $U\sim\text{Uniform}(0,1)$
2) If $U\in\left[\sum_{i=1}^kp_{k}, |
7,813 | Generating random variables from a mixture of Normal distributions | It's good practice to avoid for loops in R for performance reasons. An alternative solution which exploits the fact rnorm is vectorized:
N <- 100000
components <- sample(1:3,prob=c(0.3,0.5,0.2),size=N,replace=TRUE)
mus <- c(0,10,3)
sds <- sqrt(c(1,1,0.1))
samples <- rnorm(n=N,mean=mus[components],sd=sds[components]) | Generating random variables from a mixture of Normal distributions | It's good practice to avoid for loops in R for performance reasons. An alternative solution which exploits the fact rnorm is vectorized:
N <- 100000
components <- sample(1:3,prob=c(0.3,0.5,0.2),size= | Generating random variables from a mixture of Normal distributions
It's good practice to avoid for loops in R for performance reasons. An alternative solution which exploits the fact rnorm is vectorized:
N <- 100000
components <- sample(1:3,prob=c(0.3,0.5,0.2),size=N,replace=TRUE)
mus <- c(0,10,3)
sds <- sqrt(c(1,1,0.... | Generating random variables from a mixture of Normal distributions
It's good practice to avoid for loops in R for performance reasons. An alternative solution which exploits the fact rnorm is vectorized:
N <- 100000
components <- sample(1:3,prob=c(0.3,0.5,0.2),size= |
7,814 | Generating random variables from a mixture of Normal distributions | Conceptually, you are just picking one distribution (from $k$ possibilities) with some probability, and then generating pseudo-random variates from that distribution. In R, this would be (e.g.):
set.seed(8) # this makes the example reproducible
N = 1000 # this is how many data you want... | Generating random variables from a mixture of Normal distributions | Conceptually, you are just picking one distribution (from $k$ possibilities) with some probability, and then generating pseudo-random variates from that distribution. In R, this would be (e.g.):
se | Generating random variables from a mixture of Normal distributions
Conceptually, you are just picking one distribution (from $k$ possibilities) with some probability, and then generating pseudo-random variates from that distribution. In R, this would be (e.g.):
set.seed(8) # this makes the example repr... | Generating random variables from a mixture of Normal distributions
Conceptually, you are just picking one distribution (from $k$ possibilities) with some probability, and then generating pseudo-random variates from that distribution. In R, this would be (e.g.):
se |
7,815 | Generating random variables from a mixture of Normal distributions | Already given perfect answers, so for those who want to achieve this in Python, here is my solution:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
mu = [0, 10, 3]
sigma = [1, 1, 1]
p_i = [0.3, 0.5, 0.2]
n = 10000
x = []
for i in range(n):
z_i = np.argmax(np.random.multinomial(1, p_i))
... | Generating random variables from a mixture of Normal distributions | Already given perfect answers, so for those who want to achieve this in Python, here is my solution:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
mu = [0, 10, 3]
sigma = [1, | Generating random variables from a mixture of Normal distributions
Already given perfect answers, so for those who want to achieve this in Python, here is my solution:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
mu = [0, 10, 3]
sigma = [1, 1, 1]
p_i = [0.3, 0.5, 0.2]
n = 10000
x = []
for i i... | Generating random variables from a mixture of Normal distributions
Already given perfect answers, so for those who want to achieve this in Python, here is my solution:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
mu = [0, 10, 3]
sigma = [1, |
7,816 | How to represent an unbounded variable as number between 0 and 1 | A very common trick to do so (e.g., in connectionist modeling) is to use the hyperbolic tangent tanh as the 'squashing function".
It automatically fits all numbers into the interval between -1 and 1. Which in your case restricts the range from 0 to 1.
In r and matlab you get it via tanh().
Another squashing function i... | How to represent an unbounded variable as number between 0 and 1 | A very common trick to do so (e.g., in connectionist modeling) is to use the hyperbolic tangent tanh as the 'squashing function".
It automatically fits all numbers into the interval between -1 and 1. | How to represent an unbounded variable as number between 0 and 1
A very common trick to do so (e.g., in connectionist modeling) is to use the hyperbolic tangent tanh as the 'squashing function".
It automatically fits all numbers into the interval between -1 and 1. Which in your case restricts the range from 0 to 1.
In ... | How to represent an unbounded variable as number between 0 and 1
A very common trick to do so (e.g., in connectionist modeling) is to use the hyperbolic tangent tanh as the 'squashing function".
It automatically fits all numbers into the interval between -1 and 1. |
7,817 | How to represent an unbounded variable as number between 0 and 1 | As often, my first question was going to be "why do you want to do this", then I saw you've already answered this in the comments to the question: "I am measuring content across many different dimensions and I want to be able to make comparisons in terms of how relevant a given piece of content is. Additionally, I want... | How to represent an unbounded variable as number between 0 and 1 | As often, my first question was going to be "why do you want to do this", then I saw you've already answered this in the comments to the question: "I am measuring content across many different dimensi | How to represent an unbounded variable as number between 0 and 1
As often, my first question was going to be "why do you want to do this", then I saw you've already answered this in the comments to the question: "I am measuring content across many different dimensions and I want to be able to make comparisons in terms ... | How to represent an unbounded variable as number between 0 and 1
As often, my first question was going to be "why do you want to do this", then I saw you've already answered this in the comments to the question: "I am measuring content across many different dimensi |
7,818 | How to represent an unbounded variable as number between 0 and 1 | Any sigmoid function will work:
The top half of the logistic function (multiply by 2, subtract 1)
The error function
tanh, as suggested by Henrik. | How to represent an unbounded variable as number between 0 and 1 | Any sigmoid function will work:
The top half of the logistic function (multiply by 2, subtract 1)
The error function
tanh, as suggested by Henrik. | How to represent an unbounded variable as number between 0 and 1
Any sigmoid function will work:
The top half of the logistic function (multiply by 2, subtract 1)
The error function
tanh, as suggested by Henrik. | How to represent an unbounded variable as number between 0 and 1
Any sigmoid function will work:
The top half of the logistic function (multiply by 2, subtract 1)
The error function
tanh, as suggested by Henrik. |
7,819 | How to represent an unbounded variable as number between 0 and 1 | In addition to the good suggestions by Henrik and Simon Byrne, you could use f(x) = x/(x+1). By way of comparison, the logistic function will exaggerate differences as x grows larger. That is, the difference between f(x) and f(x+1) will be larger with the logistic function than with f(x) = x/(x+1). You may or may no... | How to represent an unbounded variable as number between 0 and 1 | In addition to the good suggestions by Henrik and Simon Byrne, you could use f(x) = x/(x+1). By way of comparison, the logistic function will exaggerate differences as x grows larger. That is, the d | How to represent an unbounded variable as number between 0 and 1
In addition to the good suggestions by Henrik and Simon Byrne, you could use f(x) = x/(x+1). By way of comparison, the logistic function will exaggerate differences as x grows larger. That is, the difference between f(x) and f(x+1) will be larger with t... | How to represent an unbounded variable as number between 0 and 1
In addition to the good suggestions by Henrik and Simon Byrne, you could use f(x) = x/(x+1). By way of comparison, the logistic function will exaggerate differences as x grows larger. That is, the d |
7,820 | How to represent an unbounded variable as number between 0 and 1 | Another customisable approach that you can explore is to simply divide all values by the maximum value and take it to the power of a positive shape value ($\gamma$) that best satisfies your desired tranformation objectives. See example below in R in which the dashed line is the simple case of dividing x by max(x):
scal... | How to represent an unbounded variable as number between 0 and 1 | Another customisable approach that you can explore is to simply divide all values by the maximum value and take it to the power of a positive shape value ($\gamma$) that best satisfies your desired tr | How to represent an unbounded variable as number between 0 and 1
Another customisable approach that you can explore is to simply divide all values by the maximum value and take it to the power of a positive shape value ($\gamma$) that best satisfies your desired tranformation objectives. See example below in R in which... | How to represent an unbounded variable as number between 0 and 1
Another customisable approach that you can explore is to simply divide all values by the maximum value and take it to the power of a positive shape value ($\gamma$) that best satisfies your desired tr |
7,821 | How to represent an unbounded variable as number between 0 and 1 | My earlier post has a method to rank between 0 and 1. Advice on classifier input correlation
However, the ranking I have used, Tmin/Tmax uses the sample min/max but you may find the population min/max more appropriate. Also look up z scores | How to represent an unbounded variable as number between 0 and 1 | My earlier post has a method to rank between 0 and 1. Advice on classifier input correlation
However, the ranking I have used, Tmin/Tmax uses the sample min/max but you may find the population min/max | How to represent an unbounded variable as number between 0 and 1
My earlier post has a method to rank between 0 and 1. Advice on classifier input correlation
However, the ranking I have used, Tmin/Tmax uses the sample min/max but you may find the population min/max more appropriate. Also look up z scores | How to represent an unbounded variable as number between 0 and 1
My earlier post has a method to rank between 0 and 1. Advice on classifier input correlation
However, the ranking I have used, Tmin/Tmax uses the sample min/max but you may find the population min/max |
7,822 | How to represent an unbounded variable as number between 0 and 1 | To add to the other answers suggesting pnorm...
For a potentially optimal method for selecting parameters I suggest this approximation for pnorm.
1.0/(1.0+exp(-1.69897*(x-mean(x))/sd(x)))
This is essentially Softmax Normalization.
Reference
Pnorm in a pinch | How to represent an unbounded variable as number between 0 and 1 | To add to the other answers suggesting pnorm...
For a potentially optimal method for selecting parameters I suggest this approximation for pnorm.
1.0/(1.0+exp(-1.69897*(x-mean(x))/sd(x)))
This is es | How to represent an unbounded variable as number between 0 and 1
To add to the other answers suggesting pnorm...
For a potentially optimal method for selecting parameters I suggest this approximation for pnorm.
1.0/(1.0+exp(-1.69897*(x-mean(x))/sd(x)))
This is essentially Softmax Normalization.
Reference
Pnorm in a ... | How to represent an unbounded variable as number between 0 and 1
To add to the other answers suggesting pnorm...
For a potentially optimal method for selecting parameters I suggest this approximation for pnorm.
1.0/(1.0+exp(-1.69897*(x-mean(x))/sd(x)))
This is es |
7,823 | How to represent an unbounded variable as number between 0 and 1 | There are two ways to implement this that I use commonly. I am always working with realtime data, so this assumes continuous input. Here's some pseudo-code:
Using a trainable minmax:
define function peak:
// keeps the highest value it has received
define function trough:
// keeps the lowest value it has receiv... | How to represent an unbounded variable as number between 0 and 1 | There are two ways to implement this that I use commonly. I am always working with realtime data, so this assumes continuous input. Here's some pseudo-code:
Using a trainable minmax:
define function p | How to represent an unbounded variable as number between 0 and 1
There are two ways to implement this that I use commonly. I am always working with realtime data, so this assumes continuous input. Here's some pseudo-code:
Using a trainable minmax:
define function peak:
// keeps the highest value it has received
de... | How to represent an unbounded variable as number between 0 and 1
There are two ways to implement this that I use commonly. I am always working with realtime data, so this assumes continuous input. Here's some pseudo-code:
Using a trainable minmax:
define function p |
7,824 | How to represent an unbounded variable as number between 0 and 1 | A very simple option is dividing each number in your data by the largest number in your data. If you have many small numbers and a few very large ones, this might not convey the information well. But it's relatively easy; if you think meaningful information is lost when you graph the data like this, you could try one... | How to represent an unbounded variable as number between 0 and 1 | A very simple option is dividing each number in your data by the largest number in your data. If you have many small numbers and a few very large ones, this might not convey the information well. Bu | How to represent an unbounded variable as number between 0 and 1
A very simple option is dividing each number in your data by the largest number in your data. If you have many small numbers and a few very large ones, this might not convey the information well. But it's relatively easy; if you think meaningful informa... | How to represent an unbounded variable as number between 0 and 1
A very simple option is dividing each number in your data by the largest number in your data. If you have many small numbers and a few very large ones, this might not convey the information well. Bu |
7,825 | How to represent an unbounded variable as number between 0 and 1 | there's a simple formula for normalization in $[0,1]$:
$$
x' = \begin{cases}
\frac{1}{ 1 + 1 / x } & \text{if } x > 0\\ 0 & \text{else}
\end{cases}
$$
$$\lim_{x\rightarrow0} x' = 0$$
$$\lim_{x\rightarrow\infty} x' = 1$$
$$\lim_{x\rightarrow1} x' = 0.5$$
Is there a name for this function? | How to represent an unbounded variable as number between 0 and 1 | there's a simple formula for normalization in $[0,1]$:
$$
x' = \begin{cases}
\frac{1}{ 1 + 1 / x } & \text{if } x > 0\\ 0 & \text{else}
\end{cases}
$$
$$\lim_{x\rightarrow0} x' = 0$$
$$\lim_{x\righta | How to represent an unbounded variable as number between 0 and 1
there's a simple formula for normalization in $[0,1]$:
$$
x' = \begin{cases}
\frac{1}{ 1 + 1 / x } & \text{if } x > 0\\ 0 & \text{else}
\end{cases}
$$
$$\lim_{x\rightarrow0} x' = 0$$
$$\lim_{x\rightarrow\infty} x' = 1$$
$$\lim_{x\rightarrow1} x' = 0.5$$
... | How to represent an unbounded variable as number between 0 and 1
there's a simple formula for normalization in $[0,1]$:
$$
x' = \begin{cases}
\frac{1}{ 1 + 1 / x } & \text{if } x > 0\\ 0 & \text{else}
\end{cases}
$$
$$\lim_{x\rightarrow0} x' = 0$$
$$\lim_{x\righta |
7,826 | Why study convex optimization for theoretical machine learning? | Machine learning algorithms use optimization all the time. We minimize loss, or error, or maximize some kind of score functions. Gradient descent is the "hello world" optimization algorithm covered on probably any machine learning course. It is obvious in the case of regression, or classification models, but even with ... | Why study convex optimization for theoretical machine learning? | Machine learning algorithms use optimization all the time. We minimize loss, or error, or maximize some kind of score functions. Gradient descent is the "hello world" optimization algorithm covered on | Why study convex optimization for theoretical machine learning?
Machine learning algorithms use optimization all the time. We minimize loss, or error, or maximize some kind of score functions. Gradient descent is the "hello world" optimization algorithm covered on probably any machine learning course. It is obvious in ... | Why study convex optimization for theoretical machine learning?
Machine learning algorithms use optimization all the time. We minimize loss, or error, or maximize some kind of score functions. Gradient descent is the "hello world" optimization algorithm covered on |
7,827 | Why study convex optimization for theoretical machine learning? | I think there are two questions here.
Why study optimization
Why convex optimization
I think @Tim has a good answer on why optimization. I strongly agree and would recommend anyone interested in machine learning to master continuous optimization. Because the optimization process / finding the better solution over ti... | Why study convex optimization for theoretical machine learning? | I think there are two questions here.
Why study optimization
Why convex optimization
I think @Tim has a good answer on why optimization. I strongly agree and would recommend anyone interested in ma | Why study convex optimization for theoretical machine learning?
I think there are two questions here.
Why study optimization
Why convex optimization
I think @Tim has a good answer on why optimization. I strongly agree and would recommend anyone interested in machine learning to master continuous optimization. Becaus... | Why study convex optimization for theoretical machine learning?
I think there are two questions here.
Why study optimization
Why convex optimization
I think @Tim has a good answer on why optimization. I strongly agree and would recommend anyone interested in ma |
7,828 | Why study convex optimization for theoretical machine learning? | As hxd1011 said, convex problems are easier to solve, both theoretically and (typically) in practice. So, even for non-convex problems, many optimization algorithms start with "step 1. reduce the problem to a convex one" (possibly inside a while loop).
A similar thing happens with nonlinear rootfinding. Usually the sol... | Why study convex optimization for theoretical machine learning? | As hxd1011 said, convex problems are easier to solve, both theoretically and (typically) in practice. So, even for non-convex problems, many optimization algorithms start with "step 1. reduce the prob | Why study convex optimization for theoretical machine learning?
As hxd1011 said, convex problems are easier to solve, both theoretically and (typically) in practice. So, even for non-convex problems, many optimization algorithms start with "step 1. reduce the problem to a convex one" (possibly inside a while loop).
A s... | Why study convex optimization for theoretical machine learning?
As hxd1011 said, convex problems are easier to solve, both theoretically and (typically) in practice. So, even for non-convex problems, many optimization algorithms start with "step 1. reduce the prob |
7,829 | Why study convex optimization for theoretical machine learning? | The most important takeaway is that machine learning is applied to problems where there is no optimal solution available. The best you can do is find a good approximation.
In contrast, when you have an optimisation problem, there is an optimal solution, but it usually cannot be found in reasonable time or with reasonab... | Why study convex optimization for theoretical machine learning? | The most important takeaway is that machine learning is applied to problems where there is no optimal solution available. The best you can do is find a good approximation.
In contrast, when you have a | Why study convex optimization for theoretical machine learning?
The most important takeaway is that machine learning is applied to problems where there is no optimal solution available. The best you can do is find a good approximation.
In contrast, when you have an optimisation problem, there is an optimal solution, bu... | Why study convex optimization for theoretical machine learning?
The most important takeaway is that machine learning is applied to problems where there is no optimal solution available. The best you can do is find a good approximation.
In contrast, when you have a |
7,830 | Why study convex optimization for theoretical machine learning? | If your interests lie in (convex) optimisation applied to deep learning (you mention transfer learning, which is widely used in practice with neural networks) applications, I strongly encourage you to consider reading chapter 8 (optimization for training deep neural networks) of http://www.deeplearningbook.org/
There i... | Why study convex optimization for theoretical machine learning? | If your interests lie in (convex) optimisation applied to deep learning (you mention transfer learning, which is widely used in practice with neural networks) applications, I strongly encourage you to | Why study convex optimization for theoretical machine learning?
If your interests lie in (convex) optimisation applied to deep learning (you mention transfer learning, which is widely used in practice with neural networks) applications, I strongly encourage you to consider reading chapter 8 (optimization for training d... | Why study convex optimization for theoretical machine learning?
If your interests lie in (convex) optimisation applied to deep learning (you mention transfer learning, which is widely used in practice with neural networks) applications, I strongly encourage you to |
7,831 | Why study convex optimization for theoretical machine learning? | As I heard from Jerome H. Friedman methods developed in Machine Learning is in fact not belong to Machine Learning community by itself.
From my point of view Machine Learning is more like a collection of various methods from another fields.
From point of view of Statistical Learning the three main questions for regress... | Why study convex optimization for theoretical machine learning? | As I heard from Jerome H. Friedman methods developed in Machine Learning is in fact not belong to Machine Learning community by itself.
From my point of view Machine Learning is more like a collection | Why study convex optimization for theoretical machine learning?
As I heard from Jerome H. Friedman methods developed in Machine Learning is in fact not belong to Machine Learning community by itself.
From my point of view Machine Learning is more like a collection of various methods from another fields.
From point of v... | Why study convex optimization for theoretical machine learning?
As I heard from Jerome H. Friedman methods developed in Machine Learning is in fact not belong to Machine Learning community by itself.
From my point of view Machine Learning is more like a collection |
7,832 | Is the sum of two white noise processes necessarily a white noise? | No, you need more (at least under Hayashi's definition of white noise). For example, the sum of two independent white noise processes is white noise.
Why is $a_t$ and $b_t$ white noise insufficient for $a_t+b_t$ to be white noise?
Following Hayashi's Econometrics, a covariance stationary process $\{z_t\}$ is defined to... | Is the sum of two white noise processes necessarily a white noise? | No, you need more (at least under Hayashi's definition of white noise). For example, the sum of two independent white noise processes is white noise.
Why is $a_t$ and $b_t$ white noise insufficient fo | Is the sum of two white noise processes necessarily a white noise?
No, you need more (at least under Hayashi's definition of white noise). For example, the sum of two independent white noise processes is white noise.
Why is $a_t$ and $b_t$ white noise insufficient for $a_t+b_t$ to be white noise?
Following Hayashi's Ec... | Is the sum of two white noise processes necessarily a white noise?
No, you need more (at least under Hayashi's definition of white noise). For example, the sum of two independent white noise processes is white noise.
Why is $a_t$ and $b_t$ white noise insufficient fo |
7,833 | Is the sum of two white noise processes necessarily a white noise? | Even simpler than @MatthewGunn's answer,
Consider $b_t = -a_t$. Obviously $c_t \equiv 0$ is not white noise -- it'd be hard to call it any kind of noise.
The broader point is, if we don't know anything about the joint distribution of $a_t$ and $b_t$, we won't be able to say what happens when we try and examine objects ... | Is the sum of two white noise processes necessarily a white noise? | Even simpler than @MatthewGunn's answer,
Consider $b_t = -a_t$. Obviously $c_t \equiv 0$ is not white noise -- it'd be hard to call it any kind of noise.
The broader point is, if we don't know anythin | Is the sum of two white noise processes necessarily a white noise?
Even simpler than @MatthewGunn's answer,
Consider $b_t = -a_t$. Obviously $c_t \equiv 0$ is not white noise -- it'd be hard to call it any kind of noise.
The broader point is, if we don't know anything about the joint distribution of $a_t$ and $b_t$, we... | Is the sum of two white noise processes necessarily a white noise?
Even simpler than @MatthewGunn's answer,
Consider $b_t = -a_t$. Obviously $c_t \equiv 0$ is not white noise -- it'd be hard to call it any kind of noise.
The broader point is, if we don't know anythin |
7,834 | Is the sum of two white noise processes necessarily a white noise? | In electronics, white noise is defined as having a flat frequency spectrum ('white') and being random ('noise'). Noise generally can be contrasted with 'interference', one or more undesired signals being picked up from elsewhere and being added to the signal of interest, and 'distortion', undesired signals being genera... | Is the sum of two white noise processes necessarily a white noise? | In electronics, white noise is defined as having a flat frequency spectrum ('white') and being random ('noise'). Noise generally can be contrasted with 'interference', one or more undesired signals be | Is the sum of two white noise processes necessarily a white noise?
In electronics, white noise is defined as having a flat frequency spectrum ('white') and being random ('noise'). Noise generally can be contrasted with 'interference', one or more undesired signals being picked up from elsewhere and being added to the s... | Is the sum of two white noise processes necessarily a white noise?
In electronics, white noise is defined as having a flat frequency spectrum ('white') and being random ('noise'). Noise generally can be contrasted with 'interference', one or more undesired signals be |
7,835 | Is the sum of two white noise processes necessarily a white noise? | if both white noise sound is traveling in same direction And if their frequency is in phase matched up, then only they get added. But, one thing i am not sure about is after adding up will it remain as white noise or it will become some other type of sound having different frequency. | Is the sum of two white noise processes necessarily a white noise? | if both white noise sound is traveling in same direction And if their frequency is in phase matched up, then only they get added. But, one thing i am not sure about is after adding up will it remain a | Is the sum of two white noise processes necessarily a white noise?
if both white noise sound is traveling in same direction And if their frequency is in phase matched up, then only they get added. But, one thing i am not sure about is after adding up will it remain as white noise or it will become some other type of so... | Is the sum of two white noise processes necessarily a white noise?
if both white noise sound is traveling in same direction And if their frequency is in phase matched up, then only they get added. But, one thing i am not sure about is after adding up will it remain a |
7,836 | Replacing outliers with mean | Clearly it's possible, but it's not clear that it could ever be a good idea.
Let's spell out several ways in which this is a limited or deficient solution:
In effect you are saying that the outlier value is completely untrustworthy, to the extent that your only possible guess is that the value should be the mean. If t... | Replacing outliers with mean | Clearly it's possible, but it's not clear that it could ever be a good idea.
Let's spell out several ways in which this is a limited or deficient solution:
In effect you are saying that the outlier v | Replacing outliers with mean
Clearly it's possible, but it's not clear that it could ever be a good idea.
Let's spell out several ways in which this is a limited or deficient solution:
In effect you are saying that the outlier value is completely untrustworthy, to the extent that your only possible guess is that the v... | Replacing outliers with mean
Clearly it's possible, but it's not clear that it could ever be a good idea.
Let's spell out several ways in which this is a limited or deficient solution:
In effect you are saying that the outlier v |
7,837 | Replacing outliers with mean | There are several problems implied by your question.
What is an "outlier"?
Should an "outlier" be replaced?
What is special about the mean as opposed to some other estimate?
How would you compensate to increase the apparent variance upon replacement by a single value that causes the variance too small?
Why not use rob... | Replacing outliers with mean | There are several problems implied by your question.
What is an "outlier"?
Should an "outlier" be replaced?
What is special about the mean as opposed to some other estimate?
How would you compensate | Replacing outliers with mean
There are several problems implied by your question.
What is an "outlier"?
Should an "outlier" be replaced?
What is special about the mean as opposed to some other estimate?
How would you compensate to increase the apparent variance upon replacement by a single value that causes the varian... | Replacing outliers with mean
There are several problems implied by your question.
What is an "outlier"?
Should an "outlier" be replaced?
What is special about the mean as opposed to some other estimate?
How would you compensate |
7,838 | Replacing outliers with mean | The proposal has numerous flaws in it. Here is perhaps the biggest.
Suppose you are gathering data, and you see these values:
$$2, 3, 1$$
The mean, so far is $6/3 = 2$.
Then comes an outlier:
$$2, 3, 1, 1000$$
So you replace it with the mean:
$$2, 3, 1, 2$$
The next number is good:
$$2, 3, 1, 2, 7$$
Now the mean is 3. ... | Replacing outliers with mean | The proposal has numerous flaws in it. Here is perhaps the biggest.
Suppose you are gathering data, and you see these values:
$$2, 3, 1$$
The mean, so far is $6/3 = 2$.
Then comes an outlier:
$$2, 3, | Replacing outliers with mean
The proposal has numerous flaws in it. Here is perhaps the biggest.
Suppose you are gathering data, and you see these values:
$$2, 3, 1$$
The mean, so far is $6/3 = 2$.
Then comes an outlier:
$$2, 3, 1, 1000$$
So you replace it with the mean:
$$2, 3, 1, 2$$
The next number is good:
$$2, 3, ... | Replacing outliers with mean
The proposal has numerous flaws in it. Here is perhaps the biggest.
Suppose you are gathering data, and you see these values:
$$2, 3, 1$$
The mean, so far is $6/3 = 2$.
Then comes an outlier:
$$2, 3, |
7,839 | Replacing outliers with mean | This article by Cousineau and Chartier discusses replacing outliers with the mean
http://www.redalyc.org/pdf/2990/299023509004.pdf
They write:
Tabachnick and Fidell (2007) suggested replacing the missing data
with the mean of the remaining data in the corresponding cell.
However, this procedure will tend to red... | Replacing outliers with mean | This article by Cousineau and Chartier discusses replacing outliers with the mean
http://www.redalyc.org/pdf/2990/299023509004.pdf
They write:
Tabachnick and Fidell (2007) suggested replacing the mi | Replacing outliers with mean
This article by Cousineau and Chartier discusses replacing outliers with the mean
http://www.redalyc.org/pdf/2990/299023509004.pdf
They write:
Tabachnick and Fidell (2007) suggested replacing the missing data
with the mean of the remaining data in the corresponding cell.
However, thi... | Replacing outliers with mean
This article by Cousineau and Chartier discusses replacing outliers with the mean
http://www.redalyc.org/pdf/2990/299023509004.pdf
They write:
Tabachnick and Fidell (2007) suggested replacing the mi |
7,840 | Replacing outliers with mean | The main thing to bear in mind when dealing with outliers is whether they're providing useful information. If you expect them to occur on a regular basis then stripping them out of the data will guarantee that your model will never predict them. Of course, it depends what you want the model to do but it's worth bearing... | Replacing outliers with mean | The main thing to bear in mind when dealing with outliers is whether they're providing useful information. If you expect them to occur on a regular basis then stripping them out of the data will guara | Replacing outliers with mean
The main thing to bear in mind when dealing with outliers is whether they're providing useful information. If you expect them to occur on a regular basis then stripping them out of the data will guarantee that your model will never predict them. Of course, it depends what you want the model... | Replacing outliers with mean
The main thing to bear in mind when dealing with outliers is whether they're providing useful information. If you expect them to occur on a regular basis then stripping them out of the data will guara |
7,841 | Replacing outliers with mean | I'm aware of two related similar approaches in statistics.
Trimmed means: when computing the mean, you drop the smallest and largest observations of your data (e.g. the top and bottom $1%$ each; you should do this symmetrically!)
Winsorization: similar to the trimmed mean, you only modify extreme observations. However... | Replacing outliers with mean | I'm aware of two related similar approaches in statistics.
Trimmed means: when computing the mean, you drop the smallest and largest observations of your data (e.g. the top and bottom $1%$ each; you | Replacing outliers with mean
I'm aware of two related similar approaches in statistics.
Trimmed means: when computing the mean, you drop the smallest and largest observations of your data (e.g. the top and bottom $1%$ each; you should do this symmetrically!)
Winsorization: similar to the trimmed mean, you only modify ... | Replacing outliers with mean
I'm aware of two related similar approaches in statistics.
Trimmed means: when computing the mean, you drop the smallest and largest observations of your data (e.g. the top and bottom $1%$ each; you |
7,842 | Replacing outliers with mean | The traditional approach for handling outliers is to simply remove them such that your model is trained only on "good" data.
Keep in mind that the mean value is affected by the presence of those outliers. If you replace outliers with the mean calculated after the outliers were removed from your dataset, it will make no... | Replacing outliers with mean | The traditional approach for handling outliers is to simply remove them such that your model is trained only on "good" data.
Keep in mind that the mean value is affected by the presence of those outli | Replacing outliers with mean
The traditional approach for handling outliers is to simply remove them such that your model is trained only on "good" data.
Keep in mind that the mean value is affected by the presence of those outliers. If you replace outliers with the mean calculated after the outliers were removed from ... | Replacing outliers with mean
The traditional approach for handling outliers is to simply remove them such that your model is trained only on "good" data.
Keep in mind that the mean value is affected by the presence of those outli |
7,843 | Replacing outliers with mean | yes the outliers can be replaced in may forms,
for example, let's take a data-set of the size of Human heights,
let's say we have some outliers like 500 cm and 400 cm then, we can just replace those data points that appear in the dataset because of some error that was caused during the recording of the data.
so the... | Replacing outliers with mean | yes the outliers can be replaced in may forms,
for example, let's take a data-set of the size of Human heights,
let's say we have some outliers like 500 cm and 400 cm then, we can just replace those | Replacing outliers with mean
yes the outliers can be replaced in may forms,
for example, let's take a data-set of the size of Human heights,
let's say we have some outliers like 500 cm and 400 cm then, we can just replace those data points that appear in the dataset because of some error that was caused during the re... | Replacing outliers with mean
yes the outliers can be replaced in may forms,
for example, let's take a data-set of the size of Human heights,
let's say we have some outliers like 500 cm and 400 cm then, we can just replace those |
7,844 | Why do we take the square root of variance to create standard deviation? | In some sense this is a trivial question, but in another, it is actually quite deep!
As others have mentioned, taking the square root implies $\operatorname{Stdev}(X)$ has the same units as $X$.
Taking the square root gives you absolute homogeneity aka absolute scalability. For any scalar $\alpha$ and random variable ... | Why do we take the square root of variance to create standard deviation? | In some sense this is a trivial question, but in another, it is actually quite deep!
As others have mentioned, taking the square root implies $\operatorname{Stdev}(X)$ has the same units as $X$.
Taki | Why do we take the square root of variance to create standard deviation?
In some sense this is a trivial question, but in another, it is actually quite deep!
As others have mentioned, taking the square root implies $\operatorname{Stdev}(X)$ has the same units as $X$.
Taking the square root gives you absolute homogenei... | Why do we take the square root of variance to create standard deviation?
In some sense this is a trivial question, but in another, it is actually quite deep!
As others have mentioned, taking the square root implies $\operatorname{Stdev}(X)$ has the same units as $X$.
Taki |
7,845 | Why do we take the square root of variance to create standard deviation? | Variance of $X$ is defined as $V(X) = E(X-E(X))^2$, so it is an expectation of a squared difference between X and its expected value.
If $X$ is time in seconds, $X-E(X)$ is in seconds, but $V(X)$ is in $\mbox{seconds}^2$ and $\sqrt{V(X)}$ is again in seconds. | Why do we take the square root of variance to create standard deviation? | Variance of $X$ is defined as $V(X) = E(X-E(X))^2$, so it is an expectation of a squared difference between X and its expected value.
If $X$ is time in seconds, $X-E(X)$ is in seconds, but $V(X)$ is i | Why do we take the square root of variance to create standard deviation?
Variance of $X$ is defined as $V(X) = E(X-E(X))^2$, so it is an expectation of a squared difference between X and its expected value.
If $X$ is time in seconds, $X-E(X)$ is in seconds, but $V(X)$ is in $\mbox{seconds}^2$ and $\sqrt{V(X)}$ is again... | Why do we take the square root of variance to create standard deviation?
Variance of $X$ is defined as $V(X) = E(X-E(X))^2$, so it is an expectation of a squared difference between X and its expected value.
If $X$ is time in seconds, $X-E(X)$ is in seconds, but $V(X)$ is i |
7,846 | Why do we take the square root of variance to create standard deviation? | The simple answer is that the units are on the same scale as the mean. Example: I estimate the mean for secondary student to be 160cm with a standard deviation (SD) of 20cm. It is intuitively easier to get a sense of the variation with the SD than the variance of 400cm^2. | Why do we take the square root of variance to create standard deviation? | The simple answer is that the units are on the same scale as the mean. Example: I estimate the mean for secondary student to be 160cm with a standard deviation (SD) of 20cm. It is intuitively easier | Why do we take the square root of variance to create standard deviation?
The simple answer is that the units are on the same scale as the mean. Example: I estimate the mean for secondary student to be 160cm with a standard deviation (SD) of 20cm. It is intuitively easier to get a sense of the variation with the SD tha... | Why do we take the square root of variance to create standard deviation?
The simple answer is that the units are on the same scale as the mean. Example: I estimate the mean for secondary student to be 160cm with a standard deviation (SD) of 20cm. It is intuitively easier |
7,847 | Why do we take the square root of variance to create standard deviation? | In more simple terms standard deviation is designed to give us a positive number that says something about the spread of our data about it's mean.
If we were to just add up the distances of all the points from the mean, then points in the positive and negative directions would combine in a way that would tend to gravi... | Why do we take the square root of variance to create standard deviation? | In more simple terms standard deviation is designed to give us a positive number that says something about the spread of our data about it's mean.
If we were to just add up the distances of all the p | Why do we take the square root of variance to create standard deviation?
In more simple terms standard deviation is designed to give us a positive number that says something about the spread of our data about it's mean.
If we were to just add up the distances of all the points from the mean, then points in the positiv... | Why do we take the square root of variance to create standard deviation?
In more simple terms standard deviation is designed to give us a positive number that says something about the spread of our data about it's mean.
If we were to just add up the distances of all the p |
7,848 | Why do we take the square root of variance to create standard deviation? | It is a historical stupidity which we continue due to intellectual laziness. They chose to square the differences from the mean in order to get rid of the minus sign. Then they took the square root so as to bring it to a scale similar to the mean.
Someone should generate new statistics, computing variance and SD using ... | Why do we take the square root of variance to create standard deviation? | It is a historical stupidity which we continue due to intellectual laziness. They chose to square the differences from the mean in order to get rid of the minus sign. Then they took the square root so | Why do we take the square root of variance to create standard deviation?
It is a historical stupidity which we continue due to intellectual laziness. They chose to square the differences from the mean in order to get rid of the minus sign. Then they took the square root so as to bring it to a scale similar to the mean.... | Why do we take the square root of variance to create standard deviation?
It is a historical stupidity which we continue due to intellectual laziness. They chose to square the differences from the mean in order to get rid of the minus sign. Then they took the square root so |
7,849 | Sample size for logistic regression? | There are several issues here.
Typically, we want to determine a minimum sample size so as to achieve a minimally acceptable level of statistical power. The sample size required is a function of several factors, primarily the magnitude of the effect you want to be able to differentiate from 0 (or whatever null you a... | Sample size for logistic regression? | There are several issues here.
Typically, we want to determine a minimum sample size so as to achieve a minimally acceptable level of statistical power. The sample size required is a function of se | Sample size for logistic regression?
There are several issues here.
Typically, we want to determine a minimum sample size so as to achieve a minimally acceptable level of statistical power. The sample size required is a function of several factors, primarily the magnitude of the effect you want to be able to differe... | Sample size for logistic regression?
There are several issues here.
Typically, we want to determine a minimum sample size so as to achieve a minimally acceptable level of statistical power. The sample size required is a function of se |
7,850 | Sample size for logistic regression? | I typically use a 15:1 rule (ratio of min(events, non-events) to number of candidate parameters in the model). More recent work found that for a more rigorous validation 20:1 is needed. More information may be found in my course handouts linked from http://hbiostat.org/rms, in particular an argument for a minimum sam... | Sample size for logistic regression? | I typically use a 15:1 rule (ratio of min(events, non-events) to number of candidate parameters in the model). More recent work found that for a more rigorous validation 20:1 is needed. More informa | Sample size for logistic regression?
I typically use a 15:1 rule (ratio of min(events, non-events) to number of candidate parameters in the model). More recent work found that for a more rigorous validation 20:1 is needed. More information may be found in my course handouts linked from http://hbiostat.org/rms, in par... | Sample size for logistic regression?
I typically use a 15:1 rule (ratio of min(events, non-events) to number of candidate parameters in the model). More recent work found that for a more rigorous validation 20:1 is needed. More informa |
7,851 | Sample size for logistic regression? | Usually, too few cases wrt. the model complexity (number of parameters) means that the models are unstable. So if you want to know whether you sample size / model complexity is OK, check whether you obtain a reasonably stable model.
There are (at least) two different kinds of instability:
The model parameters vary a l... | Sample size for logistic regression? | Usually, too few cases wrt. the model complexity (number of parameters) means that the models are unstable. So if you want to know whether you sample size / model complexity is OK, check whether you o | Sample size for logistic regression?
Usually, too few cases wrt. the model complexity (number of parameters) means that the models are unstable. So if you want to know whether you sample size / model complexity is OK, check whether you obtain a reasonably stable model.
There are (at least) two different kinds of instab... | Sample size for logistic regression?
Usually, too few cases wrt. the model complexity (number of parameters) means that the models are unstable. So if you want to know whether you sample size / model complexity is OK, check whether you o |
7,852 | Sample size for logistic regression? | Here is the actual answer from the MedCalc website user41466 wrote about
http://www.medcalc.org/manual/logistic_regression.php
Sample size considerations
Sample size calculation for logistic regression is a complex problem, but based on the work of Peduzzi et al. (1996) the following guideline for a minimum number of ... | Sample size for logistic regression? | Here is the actual answer from the MedCalc website user41466 wrote about
http://www.medcalc.org/manual/logistic_regression.php
Sample size considerations
Sample size calculation for logistic regressi | Sample size for logistic regression?
Here is the actual answer from the MedCalc website user41466 wrote about
http://www.medcalc.org/manual/logistic_regression.php
Sample size considerations
Sample size calculation for logistic regression is a complex problem, but based on the work of Peduzzi et al. (1996) the followi... | Sample size for logistic regression?
Here is the actual answer from the MedCalc website user41466 wrote about
http://www.medcalc.org/manual/logistic_regression.php
Sample size considerations
Sample size calculation for logistic regressi |
7,853 | Sample size for logistic regression? | There is no strict rules, but you can include all independent variables so long as the nominal variables dont have too many categories. You need one "beta" for all except one of the class for each nominal variable. So if a nominal variable was say "area of work" and you have 30 areas, then you'd need 29 betas.
One wa... | Sample size for logistic regression? | There is no strict rules, but you can include all independent variables so long as the nominal variables dont have too many categories. You need one "beta" for all except one of the class for each no | Sample size for logistic regression?
There is no strict rules, but you can include all independent variables so long as the nominal variables dont have too many categories. You need one "beta" for all except one of the class for each nominal variable. So if a nominal variable was say "area of work" and you have 30 ar... | Sample size for logistic regression?
There is no strict rules, but you can include all independent variables so long as the nominal variables dont have too many categories. You need one "beta" for all except one of the class for each no |
7,854 | Sample size for logistic regression? | Results from any logistic model with the number of observations per independent variable ranging from at least five to nine are reliable, especially so if results are statistically significant (Vittinghoff & McCulloch, 2007).
Vittinghoff, E., & McCulloch, C. E. 2007. Relaxing the rule of ten events per variable in log... | Sample size for logistic regression? | Results from any logistic model with the number of observations per independent variable ranging from at least five to nine are reliable, especially so if results are statistically significant (Vittin | Sample size for logistic regression?
Results from any logistic model with the number of observations per independent variable ranging from at least five to nine are reliable, especially so if results are statistically significant (Vittinghoff & McCulloch, 2007).
Vittinghoff, E., & McCulloch, C. E. 2007. Relaxing the r... | Sample size for logistic regression?
Results from any logistic model with the number of observations per independent variable ranging from at least five to nine are reliable, especially so if results are statistically significant (Vittin |
7,855 | How to teach students who fear statistics? | Try to personalize statistics. To show why understanding its concepts (even though they will forget the math, acknowledge it) is useful to them. For instance, how to interpret breast cancer test results. To quote from http://yudkowsky.net/rational/bayes:
Here's a story problem about a
situation that doctors often
... | How to teach students who fear statistics? | Try to personalize statistics. To show why understanding its concepts (even though they will forget the math, acknowledge it) is useful to them. For instance, how to interpret breast cancer test resul | How to teach students who fear statistics?
Try to personalize statistics. To show why understanding its concepts (even though they will forget the math, acknowledge it) is useful to them. For instance, how to interpret breast cancer test results. To quote from http://yudkowsky.net/rational/bayes:
Here's a story proble... | How to teach students who fear statistics?
Try to personalize statistics. To show why understanding its concepts (even though they will forget the math, acknowledge it) is useful to them. For instance, how to interpret breast cancer test resul |
7,856 | How to teach students who fear statistics? | I agree that making statistics personal/relevant is important, but that's not ultimately going to dispel the fear of the student. I think how the student feels about something often has more to do with the personality of the person teaching it, and how comfortable that person feels in the classroom, even when teaching ... | How to teach students who fear statistics? | I agree that making statistics personal/relevant is important, but that's not ultimately going to dispel the fear of the student. I think how the student feels about something often has more to do wit | How to teach students who fear statistics?
I agree that making statistics personal/relevant is important, but that's not ultimately going to dispel the fear of the student. I think how the student feels about something often has more to do with the personality of the person teaching it, and how comfortable that person ... | How to teach students who fear statistics?
I agree that making statistics personal/relevant is important, but that's not ultimately going to dispel the fear of the student. I think how the student feels about something often has more to do wit |
7,857 | How to teach students who fear statistics? | Not very much about how to deal with students' fear, but Andrew Gelman wrote an excellent book, Teaching Statistics, a bag of tricks (there's also some slides).
I like introducing a course by talking about randomness, elementary probability as found in games, causal association, permutation tests (because parametric te... | How to teach students who fear statistics? | Not very much about how to deal with students' fear, but Andrew Gelman wrote an excellent book, Teaching Statistics, a bag of tricks (there's also some slides).
I like introducing a course by talking | How to teach students who fear statistics?
Not very much about how to deal with students' fear, but Andrew Gelman wrote an excellent book, Teaching Statistics, a bag of tricks (there's also some slides).
I like introducing a course by talking about randomness, elementary probability as found in games, causal associatio... | How to teach students who fear statistics?
Not very much about how to deal with students' fear, but Andrew Gelman wrote an excellent book, Teaching Statistics, a bag of tricks (there's also some slides).
I like introducing a course by talking |
7,858 | How to teach students who fear statistics? | Frederick Mosteller said:
When I think of teaching a class, I think of five main components, not all ordinarily used in one lecture. They are
Large-scale application
Physical demonstration
Small-scale application (specific)
Statistical or probabilistic principle
Proof or plausibility argument
Tufte also mentioned (... | How to teach students who fear statistics? | Frederick Mosteller said:
When I think of teaching a class, I think of five main components, not all ordinarily used in one lecture. They are
Large-scale application
Physical demonstration
Small-sca | How to teach students who fear statistics?
Frederick Mosteller said:
When I think of teaching a class, I think of five main components, not all ordinarily used in one lecture. They are
Large-scale application
Physical demonstration
Small-scale application (specific)
Statistical or probabilistic principle
Proof or pla... | How to teach students who fear statistics?
Frederick Mosteller said:
When I think of teaching a class, I think of five main components, not all ordinarily used in one lecture. They are
Large-scale application
Physical demonstration
Small-sca |
7,859 | How to teach students who fear statistics? | This is a topic that would be of interest to members of the Isolated Statisticians group in the ASA. You are likely to get many useful responses from experienced teachers there, so I'll limit what I share here.
It's useful to understand where your students are coming from. A low-stress pre-test can help you identify ... | How to teach students who fear statistics? | This is a topic that would be of interest to members of the Isolated Statisticians group in the ASA. You are likely to get many useful responses from experienced teachers there, so I'll limit what I | How to teach students who fear statistics?
This is a topic that would be of interest to members of the Isolated Statisticians group in the ASA. You are likely to get many useful responses from experienced teachers there, so I'll limit what I share here.
It's useful to understand where your students are coming from. A... | How to teach students who fear statistics?
This is a topic that would be of interest to members of the Isolated Statisticians group in the ASA. You are likely to get many useful responses from experienced teachers there, so I'll limit what I |
7,860 | How to teach students who fear statistics? | I teach undergraduate biology students, and The Fear is rife among them. I generally start by telling them three things:
1) Statistics is not maths, it's logic. And if you're doing a science degree at a respected university, you eveidently don't have any problems with using logic to solve problems.
2) If you can add,... | How to teach students who fear statistics? | I teach undergraduate biology students, and The Fear is rife among them. I generally start by telling them three things:
1) Statistics is not maths, it's logic. And if you're doing a science degree | How to teach students who fear statistics?
I teach undergraduate biology students, and The Fear is rife among them. I generally start by telling them three things:
1) Statistics is not maths, it's logic. And if you're doing a science degree at a respected university, you eveidently don't have any problems with using ... | How to teach students who fear statistics?
I teach undergraduate biology students, and The Fear is rife among them. I generally start by telling them three things:
1) Statistics is not maths, it's logic. And if you're doing a science degree |
7,861 | How to teach students who fear statistics? | Some good answers here, but one addition.
I start off by saying "Who was the first female member of the Royal Statistical Society." I might also say "You have heard of her."
Usually no one gets it right. Then I say that it was Florence Nightingale, and I ask why she is famous. They respond about things like hygiene. I... | How to teach students who fear statistics? | Some good answers here, but one addition.
I start off by saying "Who was the first female member of the Royal Statistical Society." I might also say "You have heard of her."
Usually no one gets it ri | How to teach students who fear statistics?
Some good answers here, but one addition.
I start off by saying "Who was the first female member of the Royal Statistical Society." I might also say "You have heard of her."
Usually no one gets it right. Then I say that it was Florence Nightingale, and I ask why she is famous... | How to teach students who fear statistics?
Some good answers here, but one addition.
I start off by saying "Who was the first female member of the Royal Statistical Society." I might also say "You have heard of her."
Usually no one gets it ri |
7,862 | How to teach students who fear statistics? | "Decision making in the face of uncertainty" sounds a lot more interesting than "statistics" even though that's essentially what statistics is about. Maybe you could lead with the decision-making aspect to build motivation for the course. | How to teach students who fear statistics? | "Decision making in the face of uncertainty" sounds a lot more interesting than "statistics" even though that's essentially what statistics is about. Maybe you could lead with the decision-making asp | How to teach students who fear statistics?
"Decision making in the face of uncertainty" sounds a lot more interesting than "statistics" even though that's essentially what statistics is about. Maybe you could lead with the decision-making aspect to build motivation for the course. | How to teach students who fear statistics?
"Decision making in the face of uncertainty" sounds a lot more interesting than "statistics" even though that's essentially what statistics is about. Maybe you could lead with the decision-making asp |
7,863 | How to teach students who fear statistics? | One resource that has not been mentioned but I feel would be the best resource for this situation is the book How to Lie with Statistics by Darrell Huff. The book is full of practical examples and intuitive reasoning; it helps cement the sometimes abstract methods of statistics.
Despite having as Masters in Engineerin... | How to teach students who fear statistics? | One resource that has not been mentioned but I feel would be the best resource for this situation is the book How to Lie with Statistics by Darrell Huff. The book is full of practical examples and in | How to teach students who fear statistics?
One resource that has not been mentioned but I feel would be the best resource for this situation is the book How to Lie with Statistics by Darrell Huff. The book is full of practical examples and intuitive reasoning; it helps cement the sometimes abstract methods of statisti... | How to teach students who fear statistics?
One resource that has not been mentioned but I feel would be the best resource for this situation is the book How to Lie with Statistics by Darrell Huff. The book is full of practical examples and in |
7,864 | How to teach students who fear statistics? | No recipe covers all cases, even if common elements may be lack of confidence and, sadly, lack of competence in mathematics; and perhaps most crucially a strong cultural preconception handed down from generation to generation that statistics will be difficult, tedious and pointless, and full of weird ideas to boot.
T... | How to teach students who fear statistics? | No recipe covers all cases, even if common elements may be lack of confidence and, sadly, lack of competence in mathematics; and perhaps most crucially a strong cultural preconception handed down from | How to teach students who fear statistics?
No recipe covers all cases, even if common elements may be lack of confidence and, sadly, lack of competence in mathematics; and perhaps most crucially a strong cultural preconception handed down from generation to generation that statistics will be difficult, tedious and poi... | How to teach students who fear statistics?
No recipe covers all cases, even if common elements may be lack of confidence and, sadly, lack of competence in mathematics; and perhaps most crucially a strong cultural preconception handed down from |
7,865 | Why is the expected value named so? | Imagine that you are in Paris in 1654 and you and your friend are observing a gambling game based on sequential rolling of a six sided dice. Now, gambling is highly illegal and busts by the gendarme are quite frequent, and to be caught at a table with stacks of livre is to almost surely guarantee a lengthy stint in the... | Why is the expected value named so? | Imagine that you are in Paris in 1654 and you and your friend are observing a gambling game based on sequential rolling of a six sided dice. Now, gambling is highly illegal and busts by the gendarme a | Why is the expected value named so?
Imagine that you are in Paris in 1654 and you and your friend are observing a gambling game based on sequential rolling of a six sided dice. Now, gambling is highly illegal and busts by the gendarme are quite frequent, and to be caught at a table with stacks of livre is to almost sur... | Why is the expected value named so?
Imagine that you are in Paris in 1654 and you and your friend are observing a gambling game based on sequential rolling of a six sided dice. Now, gambling is highly illegal and busts by the gendarme a |
7,866 | Why is the expected value named so? | Excellent question. It's more subtle than it seems at first. It has to do with the random event and random variable (number, value). Your confusion stems from mixing together these two related but distinct concepts.
Let's start with an event. From the way you formulated your question, it appears that you consider the o... | Why is the expected value named so? | Excellent question. It's more subtle than it seems at first. It has to do with the random event and random variable (number, value). Your confusion stems from mixing together these two related but dis | Why is the expected value named so?
Excellent question. It's more subtle than it seems at first. It has to do with the random event and random variable (number, value). Your confusion stems from mixing together these two related but distinct concepts.
Let's start with an event. From the way you formulated your question... | Why is the expected value named so?
Excellent question. It's more subtle than it seems at first. It has to do with the random event and random variable (number, value). Your confusion stems from mixing together these two related but dis |
7,867 | Why is the expected value named so? | "Each of the values equally likely", or "some value most likely" is the definition of mode, not expected value.
Imagine we are playing a coin-tossing game. Each time I toss heads, I give you 1\$, each time I toss tails, you give me 1\$. How much money would you expect to win or loose in the long run? Amounts are equal,... | Why is the expected value named so? | "Each of the values equally likely", or "some value most likely" is the definition of mode, not expected value.
Imagine we are playing a coin-tossing game. Each time I toss heads, I give you 1\$, each | Why is the expected value named so?
"Each of the values equally likely", or "some value most likely" is the definition of mode, not expected value.
Imagine we are playing a coin-tossing game. Each time I toss heads, I give you 1\$, each time I toss tails, you give me 1\$. How much money would you expect to win or loose... | Why is the expected value named so?
"Each of the values equally likely", or "some value most likely" is the definition of mode, not expected value.
Imagine we are playing a coin-tossing game. Each time I toss heads, I give you 1\$, each |
7,868 | Why is the expected value named so? | The expected value is called so because if you average all dice rolls you expect to get this expected value in the long run. The expected value is not related to any single dice roll. | Why is the expected value named so? | The expected value is called so because if you average all dice rolls you expect to get this expected value in the long run. The expected value is not related to any single dice roll. | Why is the expected value named so?
The expected value is called so because if you average all dice rolls you expect to get this expected value in the long run. The expected value is not related to any single dice roll. | Why is the expected value named so?
The expected value is called so because if you average all dice rolls you expect to get this expected value in the long run. The expected value is not related to any single dice roll. |
7,869 | Why is the expected value named so? | From an historical point of view, the concept seemed to appear in different countries, so I would consider the use of this word as a convenient convergence between similar concepts across languages.
My starting point was the excellent Earliest Uses of Symbols in Probability and Statistics:
Expectation. A large scri... | Why is the expected value named so? | From an historical point of view, the concept seemed to appear in different countries, so I would consider the use of this word as a convenient convergence between similar concepts across languages.
| Why is the expected value named so?
From an historical point of view, the concept seemed to appear in different countries, so I would consider the use of this word as a convenient convergence between similar concepts across languages.
My starting point was the excellent Earliest Uses of Symbols in Probability and St... | Why is the expected value named so?
From an historical point of view, the concept seemed to appear in different countries, so I would consider the use of this word as a convenient convergence between similar concepts across languages.
|
7,870 | Why is the expected value named so? | Interestingly, the more general concept than expected value is location. Thus, the concept of expected value has subtle implications that are somewhat confusing.
It is reasonable to question what it means to have 3.5 as anything to do with an anticipated outcome for a die. The answer is that although the average value ... | Why is the expected value named so? | Interestingly, the more general concept than expected value is location. Thus, the concept of expected value has subtle implications that are somewhat confusing.
It is reasonable to question what it m | Why is the expected value named so?
Interestingly, the more general concept than expected value is location. Thus, the concept of expected value has subtle implications that are somewhat confusing.
It is reasonable to question what it means to have 3.5 as anything to do with an anticipated outcome for a die. The answer... | Why is the expected value named so?
Interestingly, the more general concept than expected value is location. Thus, the concept of expected value has subtle implications that are somewhat confusing.
It is reasonable to question what it m |
7,871 | What is a manifold? | In non technical terms, a manifold is a continuous geometrical structure having finite dimension : a line, a curve, a plane, a surface, a sphere, a ball, a cylinder, a torus, a "blob"... something like this :
It is a generic term used by mathematicians to say "a curve" (dimension 1) or "surface" (dimension 2), or a 3D... | What is a manifold? | In non technical terms, a manifold is a continuous geometrical structure having finite dimension : a line, a curve, a plane, a surface, a sphere, a ball, a cylinder, a torus, a "blob"... something lik | What is a manifold?
In non technical terms, a manifold is a continuous geometrical structure having finite dimension : a line, a curve, a plane, a surface, a sphere, a ball, a cylinder, a torus, a "blob"... something like this :
It is a generic term used by mathematicians to say "a curve" (dimension 1) or "surface" (d... | What is a manifold?
In non technical terms, a manifold is a continuous geometrical structure having finite dimension : a line, a curve, a plane, a surface, a sphere, a ball, a cylinder, a torus, a "blob"... something lik |
7,872 | What is a manifold? | A (topological) manifold is a space $M$ which is:
(1) "locally" "equivalent" to $\mathbb{R}^n$ for some $n$.
"Locally", the "equivalence" can be expressed via $n$ coordinate functions, $c_i: M \to \mathbb{R}$, which together form a "structure-preserving" function, $c: M \to \mathbb{R}^n$, called a chart.
(2) can be r... | What is a manifold? | A (topological) manifold is a space $M$ which is:
(1) "locally" "equivalent" to $\mathbb{R}^n$ for some $n$.
"Locally", the "equivalence" can be expressed via $n$ coordinate functions, $c_i: M \to \ | What is a manifold?
A (topological) manifold is a space $M$ which is:
(1) "locally" "equivalent" to $\mathbb{R}^n$ for some $n$.
"Locally", the "equivalence" can be expressed via $n$ coordinate functions, $c_i: M \to \mathbb{R}$, which together form a "structure-preserving" function, $c: M \to \mathbb{R}^n$, called a... | What is a manifold?
A (topological) manifold is a space $M$ which is:
(1) "locally" "equivalent" to $\mathbb{R}^n$ for some $n$.
"Locally", the "equivalence" can be expressed via $n$ coordinate functions, $c_i: M \to \ |
7,873 | What is a manifold? | In this context, the term manifold is accurate, but is unnecessarily highfalutin. Technically, a manifold is any space (set of points with a topology) that is sufficiently smooth and continuous (in a way that can, with some effort, be made mathematically well-defined).
Imagine the space of all possible values of your o... | What is a manifold? | In this context, the term manifold is accurate, but is unnecessarily highfalutin. Technically, a manifold is any space (set of points with a topology) that is sufficiently smooth and continuous (in a | What is a manifold?
In this context, the term manifold is accurate, but is unnecessarily highfalutin. Technically, a manifold is any space (set of points with a topology) that is sufficiently smooth and continuous (in a way that can, with some effort, be made mathematically well-defined).
Imagine the space of all possi... | What is a manifold?
In this context, the term manifold is accurate, but is unnecessarily highfalutin. Technically, a manifold is any space (set of points with a topology) that is sufficiently smooth and continuous (in a |
7,874 | What is a manifold? | As Bronstein and others have put it in Geometric deep learning: going beyond Euclidean data (Read the article here)
Roughly, a manifold is a space that is locally Euclidean. One of the
simplest examples is a spherical surface modeling our planet: around a
point, it seems to be planar, which has led generations of peop... | What is a manifold? | As Bronstein and others have put it in Geometric deep learning: going beyond Euclidean data (Read the article here)
Roughly, a manifold is a space that is locally Euclidean. One of the
simplest examp | What is a manifold?
As Bronstein and others have put it in Geometric deep learning: going beyond Euclidean data (Read the article here)
Roughly, a manifold is a space that is locally Euclidean. One of the
simplest examples is a spherical surface modeling our planet: around a
point, it seems to be planar, which has led... | What is a manifold?
As Bronstein and others have put it in Geometric deep learning: going beyond Euclidean data (Read the article here)
Roughly, a manifold is a space that is locally Euclidean. One of the
simplest examp |
7,875 | Why are symmetric positive definite (SPD) matrices so important? | A (real) symmetric matrix has a complete set of orthogonal eigenvectors for which the corresponding eigenvalues are are all real numbers. For non-symmetric matrices this can fail. For example, a rotation in two dimensional space has no eigenvector or eigenvalues in the real numbers, you must pass to a vector space ov... | Why are symmetric positive definite (SPD) matrices so important? | A (real) symmetric matrix has a complete set of orthogonal eigenvectors for which the corresponding eigenvalues are are all real numbers. For non-symmetric matrices this can fail. For example, a rot | Why are symmetric positive definite (SPD) matrices so important?
A (real) symmetric matrix has a complete set of orthogonal eigenvectors for which the corresponding eigenvalues are are all real numbers. For non-symmetric matrices this can fail. For example, a rotation in two dimensional space has no eigenvector or ei... | Why are symmetric positive definite (SPD) matrices so important?
A (real) symmetric matrix has a complete set of orthogonal eigenvectors for which the corresponding eigenvalues are are all real numbers. For non-symmetric matrices this can fail. For example, a rot |
7,876 | Why are symmetric positive definite (SPD) matrices so important? | With respect to optimization (because you tagged your question with the optimization tag), SPD matrices are extremely important for one simple reason - an SPD Hessian guarantees that the search direction is a descent direction. Consider the derivation of Newton's method for unconstrained optimization. First, we form ... | Why are symmetric positive definite (SPD) matrices so important? | With respect to optimization (because you tagged your question with the optimization tag), SPD matrices are extremely important for one simple reason - an SPD Hessian guarantees that the search direct | Why are symmetric positive definite (SPD) matrices so important?
With respect to optimization (because you tagged your question with the optimization tag), SPD matrices are extremely important for one simple reason - an SPD Hessian guarantees that the search direction is a descent direction. Consider the derivation of... | Why are symmetric positive definite (SPD) matrices so important?
With respect to optimization (because you tagged your question with the optimization tag), SPD matrices are extremely important for one simple reason - an SPD Hessian guarantees that the search direct |
7,877 | Why are symmetric positive definite (SPD) matrices so important? | You'll find some intuition in the many elementary ways of showing the eigenvalues of a real symmetric matrix are all real: https://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof/118640#118640
In particular, the quadratic form $x^TAx$ occurs naturally in the Rayleigh quotie... | Why are symmetric positive definite (SPD) matrices so important? | You'll find some intuition in the many elementary ways of showing the eigenvalues of a real symmetric matrix are all real: https://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eige | Why are symmetric positive definite (SPD) matrices so important?
You'll find some intuition in the many elementary ways of showing the eigenvalues of a real symmetric matrix are all real: https://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eigenvalues-elementary-proof/118640#118640
In particular, t... | Why are symmetric positive definite (SPD) matrices so important?
You'll find some intuition in the many elementary ways of showing the eigenvalues of a real symmetric matrix are all real: https://mathoverflow.net/questions/118626/real-symmetric-matrix-has-real-eige |
7,878 | Why are symmetric positive definite (SPD) matrices so important? | Geometrically, a positive definite matrix defines a metric, for instance a Riemannian metric, so we can immediately use geometric concepts.
If $x$ and $y$ are vectors and $A$ a positive definite matrix, then
$$
d(x,y) = \sqrt{(x-y)^T A (x-y)}
$$
is a metric (also called distance function).
In addition, positive d... | Why are symmetric positive definite (SPD) matrices so important? | Geometrically, a positive definite matrix defines a metric, for instance a Riemannian metric, so we can immediately use geometric concepts.
If $x$ and $y$ are vectors and $A$ a positive definite matri | Why are symmetric positive definite (SPD) matrices so important?
Geometrically, a positive definite matrix defines a metric, for instance a Riemannian metric, so we can immediately use geometric concepts.
If $x$ and $y$ are vectors and $A$ a positive definite matrix, then
$$
d(x,y) = \sqrt{(x-y)^T A (x-y)}
$$
is a m... | Why are symmetric positive definite (SPD) matrices so important?
Geometrically, a positive definite matrix defines a metric, for instance a Riemannian metric, so we can immediately use geometric concepts.
If $x$ and $y$ are vectors and $A$ a positive definite matri |
7,879 | Why are symmetric positive definite (SPD) matrices so important? | You already cited a bunch of reasons why SPD are important yet you still posted the question. So, it seems to me that you need to answer this question first: Why do positive quantities matter?
My answer is that some quantities ought to be positive in order to reconcile with our experiences or models. For instance, the... | Why are symmetric positive definite (SPD) matrices so important? | You already cited a bunch of reasons why SPD are important yet you still posted the question. So, it seems to me that you need to answer this question first: Why do positive quantities matter?
My ans | Why are symmetric positive definite (SPD) matrices so important?
You already cited a bunch of reasons why SPD are important yet you still posted the question. So, it seems to me that you need to answer this question first: Why do positive quantities matter?
My answer is that some quantities ought to be positive in ord... | Why are symmetric positive definite (SPD) matrices so important?
You already cited a bunch of reasons why SPD are important yet you still posted the question. So, it seems to me that you need to answer this question first: Why do positive quantities matter?
My ans |
7,880 | Why are symmetric positive definite (SPD) matrices so important? | There are already several answers explaining why symmetric positive definite matrices are so important, so I will provide an answer explaining why they are not as important as some people, including the authors of some of those answers, think. For the sake of simplicity, I will limit focus to symmetric matrices, and co... | Why are symmetric positive definite (SPD) matrices so important? | There are already several answers explaining why symmetric positive definite matrices are so important, so I will provide an answer explaining why they are not as important as some people, including t | Why are symmetric positive definite (SPD) matrices so important?
There are already several answers explaining why symmetric positive definite matrices are so important, so I will provide an answer explaining why they are not as important as some people, including the authors of some of those answers, think. For the sak... | Why are symmetric positive definite (SPD) matrices so important?
There are already several answers explaining why symmetric positive definite matrices are so important, so I will provide an answer explaining why they are not as important as some people, including t |
7,881 | Why are symmetric positive definite (SPD) matrices so important? | Here are two more reasons which haven't been mentioned for why positive-semidefinite matrices are important:
The graph Laplacian matrix is diagonally dominant and thus PSD.
Positive semidefiniteness defines a partial order on the set of symmetric matrices (this is the foundation of semidefinite programming). | Why are symmetric positive definite (SPD) matrices so important? | Here are two more reasons which haven't been mentioned for why positive-semidefinite matrices are important:
The graph Laplacian matrix is diagonally dominant and thus PSD.
Positive semidefiniteness | Why are symmetric positive definite (SPD) matrices so important?
Here are two more reasons which haven't been mentioned for why positive-semidefinite matrices are important:
The graph Laplacian matrix is diagonally dominant and thus PSD.
Positive semidefiniteness defines a partial order on the set of symmetric matrice... | Why are symmetric positive definite (SPD) matrices so important?
Here are two more reasons which haven't been mentioned for why positive-semidefinite matrices are important:
The graph Laplacian matrix is diagonally dominant and thus PSD.
Positive semidefiniteness |
7,882 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | Consider discrete distributions. One that is supported on $k$ values $x_1, x_2,\ldots, x_k$ is determined by non-negative probabilities $p_1, p_2,\ldots, p_k$ subject to the conditions that (a) they sum to 1 and (b) the skewness coefficient equals 0 (which is equivalent to the third central moment being zero). That l... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | Consider discrete distributions. One that is supported on $k$ values $x_1, x_2,\ldots, x_k$ is determined by non-negative probabilities $p_1, p_2,\ldots, p_k$ subject to the conditions that (a) they | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
Consider discrete distributions. One that is supported on $k$ values $x_1, x_2,\ldots, x_k$ is determined by non-negative probabilities $p_1, p_2,\ldots, p_k$ subject to the conditions that (a) they sum ... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
Consider discrete distributions. One that is supported on $k$ values $x_1, x_2,\ldots, x_k$ is determined by non-negative probabilities $p_1, p_2,\ldots, p_k$ subject to the conditions that (a) they |
7,883 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | Here is one I found at https://www.qualitydigest.com/inside/quality-insider-article/problems-skewness-and-kurtosis-part-one.html# which I find nice and reproduced in R: an inverse Burr or Dagum distribution with shape parameters $k=0.0629$ and $c=18.1484$:
$$g(x) = ckx^{-(c+1)}[1+x^{-c}]^{-(k+1)}$$
It has mean 0.5387, ... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | Here is one I found at https://www.qualitydigest.com/inside/quality-insider-article/problems-skewness-and-kurtosis-part-one.html# which I find nice and reproduced in R: an inverse Burr or Dagum distri | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
Here is one I found at https://www.qualitydigest.com/inside/quality-insider-article/problems-skewness-and-kurtosis-part-one.html# which I find nice and reproduced in R: an inverse Burr or Dagum distributi... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
Here is one I found at https://www.qualitydigest.com/inside/quality-insider-article/problems-skewness-and-kurtosis-part-one.html# which I find nice and reproduced in R: an inverse Burr or Dagum distri |
7,884 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | Consider a distribution on the positive half of the real line which increases linearly from 0 to the mode and then is exponential to the right of the mode, but is continuous at the mode.
This could be called a triangular-exponential distribution (though it does often look a bit like a shark fin).
Let $\theta$ be the lo... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | Consider a distribution on the positive half of the real line which increases linearly from 0 to the mode and then is exponential to the right of the mode, but is continuous at the mode.
This could be | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
Consider a distribution on the positive half of the real line which increases linearly from 0 to the mode and then is exponential to the right of the mode, but is continuous at the mode.
This could be cal... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
Consider a distribution on the positive half of the real line which increases linearly from 0 to the mode and then is exponential to the right of the mode, but is continuous at the mode.
This could be |
7,885 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | For zero skewness, we need
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big] = 0
$$
or, equivalently,
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big | X \leq \mu \Big] + \operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big | X \gt \mu \Big] = 0.
$$
Now, for giv... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | For zero skewness, we need
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big] = 0
$$
or, equivalently,
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big | X \l | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
For zero skewness, we need
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big] = 0
$$
or, equivalently,
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big | X \leq \... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
For zero skewness, we need
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big] = 0
$$
or, equivalently,
$$
\operatorname{E}\Big[\big(\tfrac{X-\mu}{\sigma}\big)^{\!3}\, \Big | X \l |
7,886 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | The following discrete distribution is asymmetric and has null skewness: Prob(-4)=1/3, Prob(1)=1/2, Prob(5)=1/6. I found it in the paper of Doric et al., Qual Quant (2009) 43:481-493; DOI 10.1007/s11135-007-9128-9 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | The following discrete distribution is asymmetric and has null skewness: Prob(-4)=1/3, Prob(1)=1/2, Prob(5)=1/6. I found it in the paper of Doric et al., Qual Quant (2009) 43:481-493; DOI 10.1007/s111 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
The following discrete distribution is asymmetric and has null skewness: Prob(-4)=1/3, Prob(1)=1/2, Prob(5)=1/6. I found it in the paper of Doric et al., Qual Quant (2009) 43:481-493; DOI 10.1007/s11135-0... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
The following discrete distribution is asymmetric and has null skewness: Prob(-4)=1/3, Prob(1)=1/2, Prob(5)=1/6. I found it in the paper of Doric et al., Qual Quant (2009) 43:481-493; DOI 10.1007/s111 |
7,887 | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical? | Sure. Try this:
skew= function (x, na.rm = FALSE)
{
if (na.rm) x <- x[!is.na(x)] #remove missing values
sum((x - mean(x))^3)/(length(x) * sd(x)^3) #calculate skew
}
set.seed(12929883)
x = c(rnorm(100, 1, .1), rnorm(100, 3.122, .1), rnorm(100,5, .1), rnorm(100, 4, .1), rnorm(100,1.1, .1))... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n | Sure. Try this:
skew= function (x, na.rm = FALSE)
{
if (na.rm) x <- x[!is.na(x)] #remove missing values
sum((x - mean(x))^3)/(length(x) * sd(x)^3) #calculate skew
}
set. | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
Sure. Try this:
skew= function (x, na.rm = FALSE)
{
if (na.rm) x <- x[!is.na(x)] #remove missing values
sum((x - mean(x))^3)/(length(x) * sd(x)^3) #calculate skew
}
set.seed... | Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is n
Sure. Try this:
skew= function (x, na.rm = FALSE)
{
if (na.rm) x <- x[!is.na(x)] #remove missing values
sum((x - mean(x))^3)/(length(x) * sd(x)^3) #calculate skew
}
set. |
7,888 | finding p-value in pearson correlation in R | you can use cor.test :
col1 = c(1,2,3,4)
col2 = c(1,4,3,5)
cor.test(col1,col2)
which gives :
# Pearson's product-moment correlation
# data: col1 and col2
# t = 2.117, df = 2, p-value = 0.1685
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
# -0.6451325... | finding p-value in pearson correlation in R | you can use cor.test :
col1 = c(1,2,3,4)
col2 = c(1,4,3,5)
cor.test(col1,col2)
which gives :
# Pearson's product-moment correlation
# data: col1 and col2
# t = 2.117, df = 2, p-value = 0.16 | finding p-value in pearson correlation in R
you can use cor.test :
col1 = c(1,2,3,4)
col2 = c(1,4,3,5)
cor.test(col1,col2)
which gives :
# Pearson's product-moment correlation
# data: col1 and col2
# t = 2.117, df = 2, p-value = 0.1685
# alternative hypothesis: true correlation is not equal to 0
# 95 p... | finding p-value in pearson correlation in R
you can use cor.test :
col1 = c(1,2,3,4)
col2 = c(1,4,3,5)
cor.test(col1,col2)
which gives :
# Pearson's product-moment correlation
# data: col1 and col2
# t = 2.117, df = 2, p-value = 0.16 |
7,889 | finding p-value in pearson correlation in R | If you want only the P value:
> cor.test(col1,col2)$p.value
[1] 0.1684782 | finding p-value in pearson correlation in R | If you want only the P value:
> cor.test(col1,col2)$p.value
[1] 0.1684782 | finding p-value in pearson correlation in R
If you want only the P value:
> cor.test(col1,col2)$p.value
[1] 0.1684782 | finding p-value in pearson correlation in R
If you want only the P value:
> cor.test(col1,col2)$p.value
[1] 0.1684782 |
7,890 | finding p-value in pearson correlation in R | The following will do as you ask:
library(Hmisc) # You need to download it first.
rcorr(x, type="pearson") # type can be pearson or spearman
Here x is a data frame, and rcorr returns every correlation which it is possible to form from the "x" data frame.
Or you could calculate the statistic yourself:
$$
t = \frac{\h... | finding p-value in pearson correlation in R | The following will do as you ask:
library(Hmisc) # You need to download it first.
rcorr(x, type="pearson") # type can be pearson or spearman
Here x is a data frame, and rcorr returns every correlat | finding p-value in pearson correlation in R
The following will do as you ask:
library(Hmisc) # You need to download it first.
rcorr(x, type="pearson") # type can be pearson or spearman
Here x is a data frame, and rcorr returns every correlation which it is possible to form from the "x" data frame.
Or you could calcu... | finding p-value in pearson correlation in R
The following will do as you ask:
library(Hmisc) # You need to download it first.
rcorr(x, type="pearson") # type can be pearson or spearman
Here x is a data frame, and rcorr returns every correlat |
7,891 | Can anyone clarify the concept of a "sum of random variables" | A physical, intuitive model of a random variable is to write down the name of every member of a population on one or more slips of paper--"tickets"--and put those tickets into a box. The process of thoroughly mixing the contents of the box, followed by blindly pulling out one ticket--exactly as in a lottery--models ran... | Can anyone clarify the concept of a "sum of random variables" | A physical, intuitive model of a random variable is to write down the name of every member of a population on one or more slips of paper--"tickets"--and put those tickets into a box. The process of th | Can anyone clarify the concept of a "sum of random variables"
A physical, intuitive model of a random variable is to write down the name of every member of a population on one or more slips of paper--"tickets"--and put those tickets into a box. The process of thoroughly mixing the contents of the box, followed by blind... | Can anyone clarify the concept of a "sum of random variables"
A physical, intuitive model of a random variable is to write down the name of every member of a population on one or more slips of paper--"tickets"--and put those tickets into a box. The process of th |
7,892 | Can anyone clarify the concept of a "sum of random variables" | There is no secret behind this phrase, it is as simple as you can think: if $X$ and $Y$ are two random variables, their sum is $X + Y$ and this sum is a random variable as well. If $X_1, X_2, X_3,\ldots,X_n$ and are $n$ random variables, their sum is $X_1 + X_2 + X_3 +\ldots+ X_n$ and this sum is also a random variable... | Can anyone clarify the concept of a "sum of random variables" | There is no secret behind this phrase, it is as simple as you can think: if $X$ and $Y$ are two random variables, their sum is $X + Y$ and this sum is a random variable as well. If $X_1, X_2, X_3,\ldo | Can anyone clarify the concept of a "sum of random variables"
There is no secret behind this phrase, it is as simple as you can think: if $X$ and $Y$ are two random variables, their sum is $X + Y$ and this sum is a random variable as well. If $X_1, X_2, X_3,\ldots,X_n$ and are $n$ random variables, their sum is $X_1 + ... | Can anyone clarify the concept of a "sum of random variables"
There is no secret behind this phrase, it is as simple as you can think: if $X$ and $Y$ are two random variables, their sum is $X + Y$ and this sum is a random variable as well. If $X_1, X_2, X_3,\ldo |
7,893 | Can anyone clarify the concept of a "sum of random variables" | r.v. is a relation between the occurrence of an event and a real number. Say, if it's raining the value X is 1, if it's not then 0. You can have another r.v. Y equal to 10 when it's cold, and 100 when it's hot. So, if it's raining and cold then X=1, Y=10, and X+Y=11.
X+Y values are 10 (not raining cold); 11 (raining,co... | Can anyone clarify the concept of a "sum of random variables" | r.v. is a relation between the occurrence of an event and a real number. Say, if it's raining the value X is 1, if it's not then 0. You can have another r.v. Y equal to 10 when it's cold, and 100 when | Can anyone clarify the concept of a "sum of random variables"
r.v. is a relation between the occurrence of an event and a real number. Say, if it's raining the value X is 1, if it's not then 0. You can have another r.v. Y equal to 10 when it's cold, and 100 when it's hot. So, if it's raining and cold then X=1, Y=10, an... | Can anyone clarify the concept of a "sum of random variables"
r.v. is a relation between the occurrence of an event and a real number. Say, if it's raining the value X is 1, if it's not then 0. You can have another r.v. Y equal to 10 when it's cold, and 100 when |
7,894 | Can anyone clarify the concept of a "sum of random variables" | None of these answers gives a mathematically rigorous way to think about sum of random variable. Note that $X,Y$ needs not to be defined on the same outcome domain and even if they do, $X+Y$ cannot be understood as summing up two functions. Rather, they should be first extended to the domain $\Omega_1\times \Omega_2$. ... | Can anyone clarify the concept of a "sum of random variables" | None of these answers gives a mathematically rigorous way to think about sum of random variable. Note that $X,Y$ needs not to be defined on the same outcome domain and even if they do, $X+Y$ cannot be | Can anyone clarify the concept of a "sum of random variables"
None of these answers gives a mathematically rigorous way to think about sum of random variable. Note that $X,Y$ needs not to be defined on the same outcome domain and even if they do, $X+Y$ cannot be understood as summing up two functions. Rather, they shou... | Can anyone clarify the concept of a "sum of random variables"
None of these answers gives a mathematically rigorous way to think about sum of random variable. Note that $X,Y$ needs not to be defined on the same outcome domain and even if they do, $X+Y$ cannot be |
7,895 | How can I interpret a confusion matrix | The confusion matrix is a way of tabulating the number of misclassifications, i.e., the number of predicted classes which ended up in a wrong classification bin based on the true classes.
While sklearn.metrics.confusion_matrix provides a numeric matrix, I find it more useful to generate a 'report' using the following:
... | How can I interpret a confusion matrix | The confusion matrix is a way of tabulating the number of misclassifications, i.e., the number of predicted classes which ended up in a wrong classification bin based on the true classes.
While sklear | How can I interpret a confusion matrix
The confusion matrix is a way of tabulating the number of misclassifications, i.e., the number of predicted classes which ended up in a wrong classification bin based on the true classes.
While sklearn.metrics.confusion_matrix provides a numeric matrix, I find it more useful to ge... | How can I interpret a confusion matrix
The confusion matrix is a way of tabulating the number of misclassifications, i.e., the number of predicted classes which ended up in a wrong classification bin based on the true classes.
While sklear |
7,896 | How can I interpret a confusion matrix | On y-axis confusion matrix has the actual values, and on the x-axis the values given by the predictor. Therefore, the counts on the diagonal are the number of correct predictions. And elements of the diagonal are incorrect predictions.
In your case:
>>> confusion_matrix(y_true, y_pred)
array([[2, 0, 0], # two zer... | How can I interpret a confusion matrix | On y-axis confusion matrix has the actual values, and on the x-axis the values given by the predictor. Therefore, the counts on the diagonal are the number of correct predictions. And elements of the | How can I interpret a confusion matrix
On y-axis confusion matrix has the actual values, and on the x-axis the values given by the predictor. Therefore, the counts on the diagonal are the number of correct predictions. And elements of the diagonal are incorrect predictions.
In your case:
>>> confusion_matrix(y_true, y... | How can I interpret a confusion matrix
On y-axis confusion matrix has the actual values, and on the x-axis the values given by the predictor. Therefore, the counts on the diagonal are the number of correct predictions. And elements of the |
7,897 | How can I interpret a confusion matrix | I would like to specify graphically the need to understand this. It's a simple matrix that needs to be well understood before reaching to conclusions. So here's a simplified explainable version of above answers.
0 1 2 <- Predicted
0 [2, 0, 0]
TRUE 1 [0, 0, 1]
2 [1, 0, 2]
# At 0,0: True valu... | How can I interpret a confusion matrix | I would like to specify graphically the need to understand this. It's a simple matrix that needs to be well understood before reaching to conclusions. So here's a simplified explainable version of abo | How can I interpret a confusion matrix
I would like to specify graphically the need to understand this. It's a simple matrix that needs to be well understood before reaching to conclusions. So here's a simplified explainable version of above answers.
0 1 2 <- Predicted
0 [2, 0, 0]
TRUE 1 [0, 0, 1] ... | How can I interpret a confusion matrix
I would like to specify graphically the need to understand this. It's a simple matrix that needs to be well understood before reaching to conclusions. So here's a simplified explainable version of abo |
7,898 | Line graph has too many lines, is there a better solution? | I would like to suggest a (standard) preliminary analysis to remove the principal effects of (a) variation among users, (b) the typical response among all users to the change, and (c) typical variation from one time period to the next.
A simple (but by no means the best) way to do this is to perform a few iterations of... | Line graph has too many lines, is there a better solution? | I would like to suggest a (standard) preliminary analysis to remove the principal effects of (a) variation among users, (b) the typical response among all users to the change, and (c) typical variatio | Line graph has too many lines, is there a better solution?
I would like to suggest a (standard) preliminary analysis to remove the principal effects of (a) variation among users, (b) the typical response among all users to the change, and (c) typical variation from one time period to the next.
A simple (but by no means... | Line graph has too many lines, is there a better solution?
I would like to suggest a (standard) preliminary analysis to remove the principal effects of (a) variation among users, (b) the typical response among all users to the change, and (c) typical variatio |
7,899 | Line graph has too many lines, is there a better solution? | Generally I find more than two or three lines on a single facet of a plot starts to be hard to read (although I still do it all the time). So this is an interesting example of what to do when you have something that conceptually could be a 100 facet plot. One possible way is to draw all 100 facets but instead of tryi... | Line graph has too many lines, is there a better solution? | Generally I find more than two or three lines on a single facet of a plot starts to be hard to read (although I still do it all the time). So this is an interesting example of what to do when you hav | Line graph has too many lines, is there a better solution?
Generally I find more than two or three lines on a single facet of a plot starts to be hard to read (although I still do it all the time). So this is an interesting example of what to do when you have something that conceptually could be a 100 facet plot. One... | Line graph has too many lines, is there a better solution?
Generally I find more than two or three lines on a single facet of a plot starts to be hard to read (although I still do it all the time). So this is an interesting example of what to do when you hav |
7,900 | Line graph has too many lines, is there a better solution? | One of the easiest things to is a boxplot. You can immediately see how your sample medians move and what days have the most outliers.
day <- rep(1:10, 100)
likes <- rpois(1000, 10)
d <- data.frame(day, likes)
library(ggplot2)
qplot(x=day, y=likes, data=d, geom="boxplot", group=day)
For individual analysis I suggest t... | Line graph has too many lines, is there a better solution? | One of the easiest things to is a boxplot. You can immediately see how your sample medians move and what days have the most outliers.
day <- rep(1:10, 100)
likes <- rpois(1000, 10)
d <- data.frame(day | Line graph has too many lines, is there a better solution?
One of the easiest things to is a boxplot. You can immediately see how your sample medians move and what days have the most outliers.
day <- rep(1:10, 100)
likes <- rpois(1000, 10)
d <- data.frame(day, likes)
library(ggplot2)
qplot(x=day, y=likes, data=d, geom=... | Line graph has too many lines, is there a better solution?
One of the easiest things to is a boxplot. You can immediately see how your sample medians move and what days have the most outliers.
day <- rep(1:10, 100)
likes <- rpois(1000, 10)
d <- data.frame(day |
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