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C9900 | The joint probability mass function is P(X = x and Y = y). Conditional distributions are P(X = x given Y = y), P(Y = y given X = x). Marginal distributions are P(X = x), P(Y = y). | |
C9901 | A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. because. | |
C9902 | Prior probability represents what is originally believed before new evidence is introduced, and posterior probability takes this new information into account. A posterior probability can subsequently become a prior for a new updated posterior probability as new information arises and is incorporated into the analysis. | |
C9903 | Linear discriminant analysis (LDA) is one of commonly used supervised subspace learning methods. The objective optimization is in both the ratio trace and the trace ratio forms, forming a complete framework of a new approach to jointly clustering and unsupervised subspace learning. | |
C9904 | Artificial Intelligence (AI) is a kind of simulation that involves a model intended to represent human intelligence or knowledge. An AI-based simulation model typically mimics human intelligence such as reasoning, learning, perception, planning, language comprehension, problem-solving, and decision making. | |
C9905 | How to Calculate VarianceFind the mean of the data set. Add all data values and divide by the sample size n.Find the squared difference from the mean for each data value. Subtract the mean from each data value and square the result.Find the sum of all the squared differences. Calculate the variance. | |
C9906 | If the test is statistically significant (e.g., p<0.05), then data do not follow a normal distribution, and a nonparametric test is warranted.When to Use a Nonparametric Testwhen the outcome is an ordinal variable or a rank,when there are definite outliers or.when the outcome has clear limits of detection. | |
C9907 | A commonly used rule says that a data point is an outlier if it is more than 1.5 ⋅ IQR 1.5\cdot \text{IQR} 1. 5⋅IQR1, point, 5, dot, start text, I, Q, R, end text above the third quartile or below the first quartile. Said differently, low outliers are below Q 1 − 1.5 ⋅ IQR \text{Q}_1-1.5\cdot\text{IQR} Q1−1. | |
C9908 | More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the flux through the surface, is equal to the volume integral of the divergence over the region inside the surface. | |
C9909 | An LSTM has a similar control flow as a recurrent neural network. It processes data passing on information as it propagates forward. The differences are the operations within the LSTM's cells. These operations are used to allow the LSTM to keep or forget information. | |
C9910 | In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. | |
C9911 | A parametric model is one where we assume the 'shape' of the data, and therefore only have to estimate the coefficients of the model. A non-parametric model is one where we do not assume the 'shape' of the data, and we have to estimate the most suitable form of the model, along with the coefficients. | |
C9912 | Gramin Dak Sevak- GDS. The minimum working hours of GDS Post Offices and GDS is increased to 4 hours from 3 hours. The Level 1 GDS Post Offices/GDSs will have 4 hours as working hours and Level – 2 will have 5 hours as working hours. The Point System for assessment of workload of BPMs has been abolished. | |
C9913 | The main differences between an RMS Voltage and an Average Voltage, is that the mean value of a periodic wave is the average of all the instantaneous areas taken under the curve over a given period of the waveform, and in the case of a sinusoidal quantity, this period is taken as one-half of the cycle of the wave. | |
C9914 | Statisticians often call this “statistical inference.” There are four main types of conclusions (inferences) that statisticians can draw from data: significance, estimation, generalization, and causation. In the remainder of this chapter we will focus on statistical significance. | |
C9915 | Machine learning algorithms can minimize forecasting error and do the forecast much faster and with the usage of more data. What's more, machine learning algorithms can analyze many alternative models at the same time, when in traditional econometrics you can analyze just one model at a time. | |
C9916 | The obvious difference between ANOVA and a "Multivariate Analysis of Variance" (MANOVA) is the “M”, which stands for multivariate. In basic terms, A MANOVA is an ANOVA with two or more continuous response variables. Like ANOVA, MANOVA has both a one-way flavor and a two-way flavor. | |
C9917 | Moments are used to find the central tendency(In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution), dispersion, skewness and kurtosis( the sharpness of the peak of a frequency-distribution curve).. | |
C9918 | Cosine similarity measures the similarity between two vectors of an inner product space. It is measured by the cosine of the angle between two vectors and determines whether two vectors are pointing in roughly the same direction. It is often used to measure document similarity in text analysis. | |
C9919 | There are mainly four ways of knowledge representation which are given as follows: Logical Representation. Semantic Network Representation. Frame Representation. | |
C9920 | Apriori is an algorithm for discovering itemsets (group of items) occurring frequently in a transaction database (frequent itemsets). A frequent itemset is an itemset appearing in at least minsup transactions from the transaction database, where minsup is a parameter given by the user. | |
C9921 | 6 Steps To Write Any Machine Learning Algorithm From Scratch: Perceptron Case StudyGet a basic understanding of the algorithm.Find some different learning sources.Break the algorithm into chunks.Start with a simple example.Validate with a trusted implementation.Write up your process. | |
C9922 | Sample Space is a set of all possible outcomes. It is mainly denoted as 'S'. Infinite sample spaces may be discrete or continuous. The probability of sample space is 1. | |
C9923 | Statistics is a mathematically-based field which seeks to collect and interpret quantitative data. In contrast, data science is a multidisciplinary field which uses scientific methods, processes, and systems to extract knowledge from data in a range of forms. | |
C9924 | A Neural Network has got non linear activation layers which is what gives the Neural Network a non linear element. The function for relating the input and the output is decided by the neural network and the amount of training it gets. Similarly, a complex enough neural network can learn any function. | |
C9925 | Train the network. Initializing all the weights with zeros leads the neurons to learn the same features during training. Thus, both neurons will evolve symmetrically throughout training, effectively preventing different neurons from learning different things. | |
C9926 | A bivariate distribution, whose marginals are Poisson is developed as a product of Poisson marginals with a multiplicative factor. The correlation between the two variates can be either positive or negative, depending on the value chosen for the parameter in the above multiplicative factor. | |
C9927 | Probability and the Normal Curve The normal distribution is a continuous probability distribution. This has several implications for probability. The total area under the normal curve is equal to 1. The probability that a normal random variable X equals any particular value is 0. | |
C9928 | Type II Error and Power Calculations. Recall that in hypothesis testing you can make two types of errors • Type I Error – rejecting the null when it is true. • Type II Error – failing to reject the null when it is false. = ⎛ ⎞ − − − = = = ⎛ ⎞ − | |
C9929 | Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. | |
C9930 | The Sarsa algorithm is an On-Policy algorithm for TD-Learning. The major difference between it and Q-Learning, is that the maximum reward for the next state is not necessarily used for updating the Q-values. | |
C9931 | Starting at $99.00 USD per user per month. Single-user, desktop application for Windows and Macs. Includes 12 months of technical support. Pricing information for IBM SPSS Statistics is supplied by the software provider or retrieved from publicly accessible pricing materials. | |
C9932 | In the case of a conditional probability, P(D|H), the hypothesis is fixed and the data are free to vary. Likelihood, however, is the opposite. For conditional probability, the hypothesis is treated as a given and the data are free to vary. For likelihood, the data are a given and the hypotheses vary. | |
C9933 | Regularization is a set of techniques that can prevent overfitting in neural networks and thus improve the accuracy of a Deep Learning model when facing completely new data from the problem domain. | |
C9934 | The gamma parameters can be seen as the inverse of the radius of influence of samples selected by the model as support vectors. The C parameter trades off correct classification of training examples against maximization of the decision function's margin. | |
C9935 | Naive bayes is a Generative model whereas Logistic Regression is a Discriminative model . Generative model is based on the joint probability, p( x, y), of the inputs x and the label y, and make their predictions by using Bayes rules to calculate p(y | x), and then picking the most likely label y. | |
C9936 | The Singular-Value Decomposition, or SVD for short, is a matrix decomposition method for reducing a matrix to its constituent parts in order to make certain subsequent matrix calculations simpler. | |
C9937 | Search friction [r]: The effect of obstacles to the matching the supply of a product with the demand for it that arise from the time and cost of the process of finding a match. | |
C9938 | Marginal probability: the probability of an event occurring (p(A)), it may be thought of as an unconditional probability. It is not conditioned on another event. Example: the probability that a card drawn is red (p(red) = 0.5). Another example: the probability that a card drawn is a 4 (p(four)=1/13). | |
C9939 | A normal distribution has a bell-shaped density curve described by its mean and standard deviation . The density curve is symmetrical, centered about its mean, with its spread determined by its standard deviation. | |
C9940 | Mutual information is calculated between two variables and measures the reduction in uncertainty for one variable given a known value of the other variable. A quantity called mutual information measures the amount of information one can obtain from one random variable given another. | |
C9941 | "A discrete variable is one that can take on finitely many, or countably infinitely many values", whereas a continuous random variable is one that is not discrete, i.e. "can take on uncountably infinitely many values", such as a spectrum of real numbers. | |
C9942 | Partitioning is a way of splitting numbers into smaller parts to make them easier to work with. Partitioning links closely to place value: a child will be taught to recognise that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4. | |
C9943 | Logistic regression is a powerful machine learning algorithm that utilizes a sigmoid function and works best on binary classification problems, although it can be used on multi-class classification problems through the “one vs. all” method. | |
C9944 | Sentiment analysis is the automated process of analyzing text data and sorting it into sentiments positive, negative, or neutral. Using sentiment analysis tools to analyze opinions in Twitter data can help companies understand how people are talking about their brand. | |
C9945 | Any study that attempts to predict human behavior will tend to have R-squared values less than 50%. However, if you analyze a physical process and have very good measurements, you might expect R-squared values over 90%. | |
C9946 | As a hypothetical example of systematic sampling, assume that in a population of 10,000 people, a statistician selects every 100th person for sampling. The sampling intervals can also be systematic, such as choosing a new sample to draw from every 12 hours. | |
C9947 | Three keys to managing bias when building AIChoose the right learning model for the problem. There's a reason all AI models are unique: Each problem requires a different solution and provides varying data resources. Choose a representative training data set. Monitor performance using real data. | |
C9948 | To make an ROC curve from your data you start by ranking all the values and linking each value to the diagnosis – sick or healthy. In the example in TABLE II 159 healthy people and 81 sick people are tested. The results and the diagnosis (sick Y or N) are listed and ranked based on parameter concentration. | |
C9949 | Linear regression models are used to show or predict the relationship between two variables or factors. The factor that is being predicted (the factor that the equation solves for) is called the dependent variable. | |
C9950 | Methods are commonly divided into linear and non-linear approaches. Approaches can also be divided into feature selection and feature extraction. Dimensionality reduction can be used for noise reduction, data visualization, cluster analysis, or as an intermediate step to facilitate other analyses. | |
C9951 | Z Score is free of any scale, hence it is used as a transformation technique while we need to make any variable unit free in various statistical techniques. Also, it is used to identifying outliers in a univarite way. Z-test is a statistical technique to test the Null Hypothesis against the Alternate Hypothesis. | |
C9952 | The hierarchical cluster analysis follows three basic steps: 1) calculate the distances, 2) link the clusters, and 3) choose a solution by selecting the right number of clusters. First, we have to select the variables upon which we base our clusters. | |
C9953 | Steps to follow while conducting non-parametric tests:The first step is to set up hypothesis and opt a level of significance. Now, let's look at what these two are. Set a test statistic. Set decision rule. Calculate test statistic. Compare the test statistic to the decision rule. | |
C9954 | The t-distribution cannot be calculated without a known standard deviation, while the standard normal distribution can be. | |
C9955 | When the image goes through them, the important features are kept in the convolution layers, and thanks to the pooling layers, these features are intensified and kept over the network, while discarding all the information that doesn't make a difference for the task. | |
C9956 | SVM or Support Vector Machine is a linear model for classification and regression problems. It can solve linear and non-linear problems and work well for many practical problems. The idea of SVM is simple: The algorithm creates a line or a hyperplane which separates the data into classes. | |
C9957 | A data set provides statistical significance when the p-value is sufficiently small. When the p-value is large, then the results in the data are explainable by chance alone, and the data are deemed consistent with (while not proving) the null hypothesis. | |
C9958 | First, logistic regression does not require a linear relationship between the dependent and independent variables. Second, the error terms (residuals) do not need to be normally distributed. This means that the independent variables should not be too highly correlated with each other. | |
C9959 | Advantages of Linear Regression Linear regression has a considerably lower time complexity when compared to some of the other machine learning algorithms. The mathematical equations of Linear regression are also fairly easy to understand and interpret. Hence Linear regression is very easy to master. | |
C9960 | Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor. | |
C9961 | There are 5 values above the median (upper half), the middle value is 77 which is the third quartile. The interquartile range is 77 – 64 = 13; the interquartile range is the range of the middle 50% of the data. When the sample size is odd, the median and quartiles are determined in the same way. | |
C9962 | In statistics, the logistic model (or logit model) is used to model the probability of a certain class or event existing such as pass/fail, win/lose, alive/dead or healthy/sick. | |
C9963 | 2 Model selection criteria. Akaike information criterion (AIC) (Akaike, 1974) is a fined technique based on in-sample fit to estimate the likelihood of a model to predict/estimate the future values. A good model is the one that has minimum AIC among all the other models. A lower AIC or BIC value indicates a better fit. | |
C9964 | The general formula for pointwise mutual information is given below; it is the binary logarithm of the joint probability of X = a and Y = b, divided by the product of the individual probabilities that X = a and Y = b. | |
C9965 | The Backpropagation algorithm looks for the minimum value of the error function in weight space using a technique called the delta rule or gradient descent. The weights that minimize the error function is then considered to be a solution to the learning problem. | |
C9966 | Random forests or random decision forests are an ensemble learning method for classification, regression and other tasks that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean/average prediction (regression) of the | |
C9967 | Systematic random sampling is the random sampling method that requires selecting samples based on a system of intervals in a numbered population. For example, Lucas can give a survey to every fourth customer that comes in to the movie theater. | |
C9968 | In this view, associative networks are fundamentally unorganized lists of features. By specifying what attributes to include, a frame structure promises to provide the "framework" upon which to organize and hang what a consumer knows about a product. | |
C9969 | If a p-value is lower than our significance level, we reject the null hypothesis. If not, we fail to reject the null hypothesis. | |
C9970 | The Regression Tree Algorithm can be used to find one model that results in good predictions for the new data. | |
C9971 | If X takes values in [a, b] and Y takes values in [c, d] then the pair (X, Y ) takes values in the product [a, b] × [c, d]. The joint probability density function (joint pdf) of X and Y is a function f(x, y) giving the probability density at (x, y). | |
C9972 | Here are five ways to identify segments.Cross-Tab. Cross-tabbing is the process of examining more than one variable in the same table or chart (“crossing” them). Cluster Analysis. Factor Analysis. Latent Class Analysis (LCA) Multidimensional Scaling (MDS) | |
C9973 | Creating the Regression LineDEFINITIONS:b1 - This is the SLOPE of the regression line. b0 - This is the intercept of the regression line with the y-axis. Y-hat = b0 + b1(x) - This is the sample regression line. | |
C9974 | In Chi-Square goodness of fit test, the term goodness of fit is used to compare the observed sample distribution with the expected probability distribution. Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits the empirical distribution. | |
C9975 | The correlation is the covariance divided by the product of the standard deviations. Therefore the correlation is the gradient of the regression line multiplied by the ratio of the standard deviations. If these standard deviations are equal the correlation is equal to the gradient. | |
C9976 | In convolutional networks, multiple filters are taken to slice through the image and map them one by one and learn different portions of an input image. Imagine a small filter sliding left to right across the image from top to bottom and that moving filter is looking for, say, a dark edge. | |
C9977 | Weight is the parameter within a neural network that transforms input data within the network's hidden layers. A neural network is a series of nodes, or neurons. Within each node is a set of inputs, weight, and a bias value. | |
C9978 | Multivariate testing uses the same core mechanism as A/B testing, but compares a higher number of variables, and reveals more information about how these variables interact with one another. As in an A/B test, traffic to a page is split between different versions of the design. | |
C9979 | Rule of Multiplication The probability that Events A and B both occur is equal to the probability that Event A occurs times the probability that Event B occurs, given that A has occurred. | |
C9980 | The world is fast evolving, with Artificial intelligence (AI) at the forefront in changing the world and the way we live. This means that with AI, many of our everyday activities can now be carried out effectively by programmed machine technology. | |
C9981 | Examples of such greedy algorithms are Kruskal's algorithm and Prim's algorithm for finding minimum spanning trees, and the algorithm for finding optimum Huffman trees. Greedy algorithms appear in network routing as well. | |
C9982 | Median filtering is generally less sensitive to outliers than mean filtering. If you don't believe that the Gaussian assumption of the data will hold very accurately, then a median filter may be the better choice. However, if the Gaussian assumption holds pretty well, then the median filter may be less efficient. | |
C9983 | Given a probability density function, we define the cumulative distribution function (CDF) as follows. The cumulative distribution function (CDF) of a random variable X is denoted by F(x), and is defined as F(x) = Pr(X ≤ x). where xn is the largest possible value of X that is less than or equal to x. | |
C9984 | If your regression model contains independent variables that are statistically significant, a reasonably high R-squared value makes sense. Correspondingly, the good R-squared value signifies that your model explains a good proportion of the variability in the dependent variable. | |
C9985 | First consider the case when X and Y are both discrete. Then the marginal pdf's (or pmf's = probability mass functions, if you prefer this terminology for discrete random variables) are defined by fY(y) = P(Y = y) and fX(x) = P(X = x). The joint pdf is, similarly, fX,Y(x,y) = P(X = x and Y = y). | |
C9986 | Weighted kNN is a modified version of k nearest neighbors. The simplest method is to take the majority vote, but this can be a problem if the nearest neighbors vary widely in their distance and the closest neighbors more reliably indicate the class of the object. | |
C9987 | A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is actually true in the population; a type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is actually false in the population. | |
C9988 | Given any collection of pairs of numbers (except when all the x-values are the same) and the corresponding scatter diagram, there always exists exactly one straight line that fits the data better than any other, in the sense of minimizing the sum of the squared errors. It is called the least squares regression line. | |
C9989 | Poisson distribution is used to model the # of events in the future, Exponential distribution is used to predict the wait time until the very first event, and Gamma distribution is used to predict the wait time until the k-th event. | |
C9990 | Content validity is different from face validity, which refers not to what the test actually measures, but to what it superficially appears to measure. In clinical settings, content validity refers to the correspondence between test items and the symptom content of a syndrome. | |
C9991 | False Alarm Rate. A false alarm is “an erroneous radar target detection decision caused by noise or other interfering signals exceeding the detection threshold”. In general, it is an indication of the presence of radar target when there is no valid aim. | |
C9992 | Process of Calculating the Histogram of Oriented Gradients (HOG)Step 1: Preprocess the Data (64 x 128) This is a step most of you will be pretty familiar with. Step 2: Calculating Gradients (direction x and y) Step 3: Calculate the Magnitude and Orientation. | |
C9993 | Under the hood, these RDDs are stored in partitions on different cluster nodes. Partition basically is a logical chunk of a large distributed data set. It provides the possibility to distribute the work across the cluster, divide the task into smaller parts, and reduce memory requirements for each node. | |
C9994 | TL;DR – The train_test_split function is for splitting a single dataset for two different purposes: training and testing. | |
C9995 | The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1. | |
C9996 | K-NN is a lazy learner because it doesn't learn a discriminative function from the training data but “memorizes” the training dataset instead. For example, the logistic regression algorithm learns its model weights (parameters) during training time. A lazy learner does not have a training phase. | |
C9997 | Weights and biases (commonly referred to as w and b) are the learnable parameters of a machine learning model. When the inputs are transmitted between neurons, the weights are applied to the inputs along with the bias. A neuron. Weights control the signal (or the strength of the connection) between two neurons. | |
C9998 | The More Formal Formula You can solve these types of problems using the steps above, or you can us the formula for finding the probability for a continuous uniform distribution: P(X) = d – c / b – a. This is also sometimes written as: P(X) = x2 – x1 / b – a. | |
C9999 | Predictive analytics are used to determine customer responses or purchases, as well as promote cross-sell opportunities. Predictive models help businesses attract, retain and grow their most profitable customers. Improving operations. Many companies use predictive models to forecast inventory and manage resources. |
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