markdown stringlengths 0 37k | code stringlengths 1 33.3k | path stringlengths 8 215 | repo_name stringlengths 6 77 | license stringclasses 15
values |
|---|---|---|---|---|
Now plot stocks | plt.figure(figsize=[10,9])
plt.subplot(3,1,1)
plt.plot(X_path[:,0])
plt.title(r'Employment')
plt.subplot(3,1,2)
plt.plot(X_path[:,1])
plt.title(r'Unemployment')
plt.subplot(3,1,3)
plt.plot(X_path.sum(1))
plt.title(r'Labor Force') | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
And how the rates evolve: | plt.figure(figsize=[10,6])
plt.subplot(2,1,1)
plt.plot(x_path[:,0])
plt.hlines(xbar[0],0,T,'r','--')
plt.title(r'Employment Rate')
plt.subplot(2,1,2)
plt.plot(x_path[:,1])
plt.hlines(xbar[1],0,T,'r','--')
plt.title(r'Unemployment Rate') | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
We see that it takes 20 periods for the economy to converge to it's new steady state levels
Exercise 2
This next exercise has the economy expriencing a boom in entrances to the labor market and then later returning to the original levels. For 20 periods the economy has a new entry rate into the labor market | bhat = 0.003
T_hat = 20
LM1 = LakeModel(lamb,alpha,bhat,d) | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
We simulate for 20 periods at the new parameters | X_path1 = np.vstack(LM1.simulate_stock_path(x0*N0,T_hat)) # simulate stocks
x_path1 = np.vstack(LM1.simulate_rate_path(x0,T_hat)) # simulate rates | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
Now using the state after 20 periods for the new initial conditions we simulate for the additional 30 periods | X_path2 = np.vstack(LM0.simulate_stock_path(X_path1[-1,:2],T-T_hat+1)) # simulate stocks
x_path2 = np.vstack(LM0.simulate_rate_path(x_path1[-1,:2],T-T_hat+1)) # simulate rates | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
Finally we combine these two paths and plot | x_path = np.vstack([x_path1,x_path2[1:]]) # note [1:] to avoid doubling period 20
X_path = np.vstack([X_path1,X_path2[1:]]) # note [1:] to avoid doubling period 20
plt.figure(figsize=[10,9])
plt.subplot(3,1,1)
plt.plot(X_path[:,0])
plt.title(r'Employment')
plt.subplot(3,1,2)
plt.plot(X_path[:,1])
plt.title(r'Unemploym... | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
And the rates: | plt.figure(figsize=[10,6])
plt.subplot(2,1,1)
plt.plot(x_path[:,0])
plt.hlines(x0[0],0,T,'r','--')
plt.title(r'Employment Rate')
plt.subplot(2,1,2)
plt.plot(x_path[:,1])
plt.hlines(x0[1],0,T,'r','--')
plt.title(r'Unemployment Rate') | solutions/lakemodel_solutions.ipynb | gxxjjj/QuantEcon.py | bsd-3-clause |
This is a very similar problem to the prediction intervals we had before. We know that $p(\mu - \bar{x})$ follows a $T(0, \sigma_x /\sqrt{N}, N - 1)$ distribution and we can use the same idea as $Z$-scores as we did for prediction intervals
$$T(y) = \frac{y - 0}{\sigma_x / \sqrt{N}}$$
The 'mean' our error in the popula... | import scipy.stats
#The lower T Value. YOU MUST GIVE THE SAMPLE NUMBER
print(scipy.stats.t.ppf(0.025, 4))
print(scipy.stats.t.ppf(0.975, 4)) | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
$$T_{low} = \frac{-y - 0}{\sigma_x / \sqrt{N}}$$
$$T_{low} = -\frac{y}{\sigma_x / \sqrt{N}}$$
$$y = -T_{low}\frac{\sigma_x}{\sqrt{N}}$$ | print(-scipy.stats.t.ppf(0.025, 4) * 3 / np.sqrt(5)) | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
The final answer is $P(45 - 3.72 < 45 < 45 + 3.72) = 0.95$ or $45\pm 3.72$
Computing Confidence Interval for Error in Population Mean Steps
Is the sample size greater than 25 OR do you know the true (population) standard deviation? If so, then use standard normal ($Z$) otherwise the $t$-distribution for your sample si... | # DO NOT COPY, JUST GENERATING DATA FOR EXAMPLE
data = scipy.stats.norm.rvs(size=100, scale=15, loc=50)
#Check if sample size is big enough.
#This code will cause an error if it's not
assert len(data) > 25
CI = 0.95
sample_mean = np.mean(data)
#The second argument specifies what the denominator should be (N - x),
#w... | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
Is that low? Well, remember that our error in the mean follows standard deviation divided by the root of number of samples.
Shortcut Method For $t$-Distribution
Here's how to quickly do these steps in Python for sample size less than 25 | # DO NOT COPY, THIS JUST GENERATES DATA FOR EXAMPLE
data = scipy.stats.norm.rvs(size=4, scale=15, loc=50)
CI = 0.95
sample_mean = np.mean(data)
sample_var = np.var(data, ddof=1)
T = scipy.stats.t.ppf((1 - CI) / 2, df=len(data)-1)
y = -T * np.sqrt(sample_var / len(data))
print('{} +/ {}'.format(sample_mean, y))
... | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
Example of Prediction Intervals
I know that the thickness of a metal slab is distributed according to ${\cal N}(3.4, 0.75)$. Construct a prediction interval so that a randomly chosen metal slab will lie within it 95% confidence.
$$P( \mu - y < x < \mu + y) = 0.95$$
This is a prediction interval, so we're computing a in... | #Notice it is 95%, so the interval goes from
#5% to 95% containing 90% of probability
T = scipy.stats.t.ppf(0.95, df=6-1)
print(T) | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
$$ y = \frac{1.25}{\sqrt{6}} 2.015 = 1.028 $$
$$\mu = 3.65 \pm 1.028$$
The population mean of the slabs is $3.65 \pm 1.028$ with 90% confidence.
Example 2 of error in population mean with unknown $\sigma$
I measure the thickness of 25 metal slabs and find that $\bar{x}$, the sample mean, is 3.42 and the sample standard... | #make some points for plot
N = 5
x = np.linspace(-5,5, 1000)
T = ss.t.ppf(0.10, df=N-1)
y = ss.t.pdf(x, df=N-1)
plt.plot(x,y)
plt.fill_between(x, y, where= x > T)
plt.text(0,np.max(y) / 3, 'Area=0.90', fontdict={'size':14}, horizontalalignment='center')
plt.axvline(T, linestyle='--', color='orange')
plt.xticks([T], [... | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
Lower Interval (Upper-Bound)
A lower interval covers the lower x% of probability mass. It is defined with an upper bound like so: $(-\infty, y)$. An example is below: | #make some points for plot
N = 5
x = np.linspace(-5,5, 1000)
T = ss.t.ppf(0.90, df=N-1)
y = ss.t.pdf(x, df=N-1)
plt.plot(x,y)
plt.fill_between(x, y, where= x < T)
plt.text(0,np.max(y) / 3, 'Area=0.90', fontdict={'size':14}, horizontalalignment='center')
plt.axvline(T, linestyle='--', color='orange')
plt.xticks([T], [... | unit_8/lectures/lecture_2.ipynb | whitead/numerical_stats | gpl-3.0 |
Concepts | concepts = pd.read_csv('data/concepts.csv')
concepts.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Blocks | blocks = pd.read_csv('data/blocks.csv')
blocks.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Instructions | instructions = pd.read_csv('data/instructions.csv')
instructions.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Tasks | tasks = pd.read_csv('data/tasks.csv')
tasks.head(3) | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Students | students = pd.read_csv('data/students.csv')
students.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Task Instances | task_instances = pd.read_csv('data/task-instances.csv')
task_instances.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Attempts | attempts = pd.read_csv('data/attempts.csv')
attempts.head() | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Analysis Example
Problem: Find median of a task solving time for each programming concept. | programming_concepts = concepts[concepts.type == 'programming']
programming_concepts
solved_instances = task_instances[task_instances.solved]
instances_concepts = pd.merge(solved_instances, tasks, on='task_id')[['time_spent', 'concepts_ids']]
instances_concepts.head()
# unpack concepts IDs
from ast import literal_eva... | analysis/demo/demo.ipynb | adaptive-learning/flocs | gpl-2.0 |
Let's start with a string lightning round to warm up. What are the lengths of the strings below?
For each of the five strings below, predict what len() would return when passed that string. Use the variable length to record your answer, then run the cell to check whether you were right.
0a. | a = ""
length = ____
q0.a.check() | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
0b. | b = "it's ok"
length = ____
q0.b.check() | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
0c. | c = 'it\'s ok'
length = ____
q0.c.check() | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
0d. | d = """hey"""
length = ____
q0.d.check() | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
0e. | e = '\n'
length = ____
q0.e.check() | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
1.
There is a saying that "Data scientists spend 80% of their time cleaning data, and 20% of their time complaining about cleaning data." Let's see if you can write a function to help clean US zip code data. Given a string, it should return whether or not that string represents a valid zip code. For our purposes, a val... | def is_valid_zip(zip_code):
"""Returns whether the input string is a valid (5 digit) zip code
"""
pass
# Check your answer
q1.check()
#%%RM_IF(PROD)%%
def is_valid_zip(zip_code):
"""Returns whether the input string is a valid (5 digit) zip code
"""
return len(zip_code) == 5 and zip_code.isdigi... | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
2.
A researcher has gathered thousands of news articles. But she wants to focus her attention on articles including a specific word. Complete the function below to help her filter her list of articles.
Your function should meet the following criteria:
Do not include documents where the keyword string shows up only as ... | def word_search(doc_list, keyword):
"""
Takes a list of documents (each document is a string) and a keyword.
Returns list of the index values into the original list for all documents
containing the keyword.
Example:
doc_list = ["The Learn Python Challenge Casino.", "They bought a car", "Casin... | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
3.
Now the researcher wants to supply multiple keywords to search for. Complete the function below to help her.
(You're encouraged to use the word_search function you just wrote when implementing this function. Reusing code in this way makes your programs more robust and readable - and it saves typing!) | def multi_word_search(doc_list, keywords):
"""
Takes list of documents (each document is a string) and a list of keywords.
Returns a dictionary where each key is a keyword, and the value is a list of indices
(from doc_list) of the documents containing that keyword
>>> doc_list = ["The Learn Pytho... | notebooks/python/raw/ex_6.ipynb | Kaggle/learntools | apache-2.0 |
Synthesize the dataset
Create 1000 random integers between 0, 100 for X and create y such that
$$
y = \beta_{0} + \beta_{1}X + \epsilon
$$
where
$$
\beta_{0} = 30 \ and \ \beta_{1} = 1.8 \ and \ \epsilon \ = \ standard \ normal \ error
$$ | rand_1kx = np.random.randint(0,100,1000)
x_mean = np.mean(rand_1kx)
x_sd = np.std(rand_1kx)
x_mean
pop_intercept = 30
pop_slope = 1.8
error_boost = 10
pop_error = np.random.standard_normal(size = rand_1kx.size) * error_boost
# I added an error booster since without it, the correlation was too high.
y = pop_intercept ... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Make a scatter plot of X and y variables. | sns.jointplot(rand_1kx, y) | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
X and y follow uniform distribution, but the error $\epsilon$ is generated from standard normal distribution with a boosting factor. Let us plot its histogram to verify the distribution | sns.distplot(pop_error) | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Predict using population
Let us predict the coefficients and intercept when using the whole dataset. We will compare this approach with CLT approach of breaking into multiple subsets and averaging the coefficients and intercepts
Using whole population | from sklearn.linear_model import LinearRegression
X_train_full = rand_1kx.reshape(-1,1)
y_train_full = y.reshape(-1,1)
y_train_full.shape
lm.fit(X_train, y_train)
#print the linear model built
predicted_pop_slope = lm.coef_[0][0]
predicted_pop_intercept = lm.intercept_[0]
print("y = " + str(predicted_pop_slope) + "... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Prediction with 66% of data | from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(rand_1kx, y, test_size=0.33)
print(X_train.size)
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
X_train = X_train.reshape(-1,1)
X_test = X_test.reshape(-1,1)
y_train = y_train.reshape(-1... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Perform predictions and plot the charts | y_predicted = lm.predict(X_test)
residuals = y_test - y_predicted | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Fitted vs Actual scatter | jax = sns.jointplot(y_test, y_predicted)
jax.set_axis_labels(xlabel='Y', ylabel='Predicted Y')
dax = sns.distplot(residuals)
dax.set_title('Distribution of residuals')
jax = sns.jointplot(y_predicted, residuals)
jax.set_axis_labels(xlabel='Predicted Y', ylabel='Residuals')
jax = sns.jointplot(y_test, residuals)
jax.... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Predict using multiple samples | pop_df = pd.DataFrame(data={'x':rand_1kx, 'y':y})
pop_df.head()
pop_df.shape | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Select 50 samples of size 200 and perform regression | sample_slopes = []
sample_intercepts = []
for i in range(0,50):
# perform a choice on dataframe index
sample_index = np.random.choice(pop_df.index, size=50)
# select the subset using that index
sample_df = pop_df.iloc[sample_index]
# convert to numpy and reshape the matrix for lm.fit
... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Plot the distribution of sample slopes and intercepts | mean_sample_slope = np.mean(sample_slopes)
mean_sample_intercept = np.mean(sample_intercepts)
fig, ax = plt.subplots(1,2, figsize=(15,6))
# plot sample slopes
sns.distplot(sample_slopes, ax=ax[0])
ax[0].set_title('Distribution of sample slopes. Mean: '
+ str(round(mean_sample_slope, 2)))
ax[0].axvlin... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Conclusion
Here we compare the coefficients and intercepts obtained by different methods to see how CLT adds up. | print("Predicting using population")
print("----------------------------")
print("Error in intercept: {}".format(pop_intercept - predicted_pop_intercept))
print("Error in slope: {}".format(pop_slope - predicted_pop_slope))
print("\n\nPredicting using subset")
print("----------------------------")
print("Error in inter... | islr/verifying_clt_in_regression.ipynb | AtmaMani/pyChakras | mit |
Likewise, as before we need to create an event parth function and a severity level function. | event_names = ["event_%i"%i for i in range(n_events)]
def event_path(x): # Returns a list of strings with 3 elements
return ["Type_%i"%(x/N) for N in [50, 10]]+[event_names[x]]
def severity_level(x): # returns 3 different severity levels: 0, 1, 2
return x-(x/3)*3 | docs/visISC_query_dialog_example.ipynb | STREAM3/visisc | bsd-3-clause |
Next, we need to make an subclass or an instance of the visisc.EventSelectionQuery. This class uses the <a href="http://docs.enthought.com/traits">Traits</a> library which is also used by <a href="http://docs.enthought.com/mayavi/mayavi/">Mayavi</a>, the 3D visualization library that we use for visualizing the data. In... | class MySelectionQuery(visisc.EventSelectionQuery):
def __init__(self):
self.list_of_source_ids = [i for i in range(n_sources*n_classes)]
# Below: a list of pairs with id and name, where the name is shown in the GUI while the id is put into teh selection.
self.list_of_source_classes = [(i, ... | docs/visISC_query_dialog_example.ipynb | STREAM3/visisc | bsd-3-clause |
Given that we have the query class, we can now create and open a query selection dialog where it is possible to customize the labels for source classes and the severity levels. | query = MySelectionQuery()
dialog = visisc.EventSelectionDialog(
query,
source_class_label="Select Machine Types",
severity_level_label="Select Event Severity Types"
) | docs/visISC_query_dialog_example.ipynb | STREAM3/visisc | bsd-3-clause |
For opening the window, we can the call. However, simarly to previous visualization examples, we have to run it outside the Jupyter notebook by calling ipython directly.
dialog.configure_traits() | !ipython --matplotlib=wx --gui=wx -i visISC_query_dialog_example.py | docs/visISC_query_dialog_example.ipynb | STREAM3/visisc | bsd-3-clause |
It's in a zip format, so unzip it: | !unzip 2013-Q1-Trips-History-Data.zip | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
How big is it? | !wc 2013-Q1-Trips-History-Data.csv | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
What are its columns? | !csvcut -n 2013-Q1-Trips-History-Data.csv | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Okay, let's have a look. | !head -5 2013-Q1-Trips-History-Data.csv | csvlook | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Ah, that's kinda wordy. Let's cut out that first column, which we can compute for ourselves later. | !head 2013-Q1-Trips-History-Data.csv | csvcut -C1 | csvlook | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
That's a little bit cleaner, and the rest of the data should be useful. Let's clean up the data by removing that column and renaming the headers so they're a little easier to query. | !csvcut -C1 2013-Q1-Trips-History-Data.csv | \
header -r "start_date,end_date,start_station,end_station,bike_id,sub_type" \
> bikeshare.csv | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Make sure you haven't lost anything! | !wc bikeshare.csv | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Prepping and loading data into the database
Alright, then, let's get loading. | %load_ext sql | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
NOTE: See a bunch of ShimWarnings with a pink background? That's normal. It's just a heads-up about ongoing changes to IPython/Jupyter code. You can keep going.
First, we create a database in mysql. Note: you can do the same thing on the command line by issuing the CREATE DATABASE command part before the pipe withi... | !echo "CREATE DATABASE bikedb" | mysql --user=mysqluser --password=mysqlpass | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Here's how we connect the notebook up to the mysql database using a username and password. Remember that this shorthand version is possible thanks to the excellent ipython-sql Jupyter extension that we're using, otherwise you'd have to establish the connection, get a cursor, etc., like you've done explicitly in python... | %sql mysql://mysqluser:mysqlpass@localhost/bikedb | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Very easy, no?
First, clean up if we're not running this for the first time. | %%sql
DROP TABLE IF EXISTS bikeshare; | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Next, create a table schema using DDL. | %%sql
CREATE TABLE bikeshare (
start_date DATETIME,
end_date DATETIME,
start_station VARCHAR(100),
end_station VARCHAR(100),
bike_id CHAR(7),
sub_type CHAR(10)
) | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Just to verify it worked: | %%sql
SELECT COUNT(*)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
It worked! We just don't have any data in there yet.
Now we load the data using LOAD DATA INFILE. You can do pretty much the same thing from the bash shell using mysqlimport and a bunch of options. It'll read better here in the notebook with the options spelled out.
Docs for LOAD DATA INFILE are available at https:/... | %%sql
LOAD DATA INFILE '/vagrant/bikeshare.csv'
REPLACE
INTO TABLE bikeshare
FIELDS TERMINATED BY ','
OPTIONALLY ENCLOSED BY '"'
IGNORE 1 LINES
(@start_date, @end_date, start_station, end_station, bike_id, sub_type)
SET start_date = STR_TO_DATE(@start_date, '%c/%e/%Y %k:%i'),
end_date = STR_TO_DATE(@end_dat... | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Note: if the above command fails for you with a "file not found" error, please read these notes about apparmor. Follow that advice, and add a line like it shows, e.g.:
/vagrant/* r
...to the file, or whatever path you have your data on, reload apparmor, and try again. I had to do this, and it worked perfectly after I... | %%sql
SELECT COUNT(*)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Looks good! Let's look at the data a little. | %%sql
SELECT *
FROM bikeshare
LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
How does MySQL construct this query, or more specifically, what's its execution plan? We can find out with EXPLAIN.
For more about how to read MySQL 5.5's query plan, see https://dev.mysql.com/doc/refman/5.5/en/execution-plan-information.html. | %%sql
EXPLAIN SELECT COUNT(*)
FROM bikeshare
LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
This says "using no keys, we're going to just scan roughly 395,390 rows, sans indexes, to answer this query." | %%sql
SELECT MAX(start_date)
FROM bikeshare
%%sql
EXPLAIN SELECT MAX(start_date)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Pretty much the same thing. You can't get the max without looking at all of the values if there is no index. | %%sql
SELECT COUNT(*)
FROM bikeshare
WHERE start_station LIKE "%dupont%"
%%sql
EXPLAIN SELECT COUNT(*)
FROM bikeshare
WHERE start_station LIKE "%dupont%" | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Now we see "using where" under "extra", so we know there's a filter operation, but that's about the only change. What if we add more things to filter on? | %%sql
EXPLAIN SELECT start_station, end_station, COUNT(*)
FROM bikeshare
WHERE start_station LIKE "%dupont%"
AND end_station LIKE "%21st%"
AND start_date LIKE "2013-02-14%"
GROUP BY start_station, end_station
ORDER BY start_station, end_station | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Ah, some more info - it looks like it's using a temporary relation to store intermediate results, perhaps for the GROUP BY, then a sort to handle ORDER BY.
Still no indexes, though. Let's change that. | %%sql
CREATE INDEX idx_start_station ON bikeshare (start_station)
%%sql
EXPLAIN SELECT start_station, end_station, COUNT(*)
FROM bikeshare
WHERE start_station LIKE "21st%"
AND start_date LIKE "2013-02-14%"
GROUP BY start_station, end_station
ORDER BY start_station, end_station | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
I changed the query a little bit to use the index, do you see the difference? It found search keys in the index, and the row count went down by an order of magnitude. That's the power of indexes.
It helps even on simple queries like this. | %%sql
EXPLAIN SELECT DISTINCT start_station
FROM bikeshare
ORDER BY start_station | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
What's that 201 value for rows? Maybe the actual count of distinct values. We can test that: | %%sql
SELECT COUNT(*)
FROM (
SELECT DISTINCT start_station
FROM bikeshare
) made_up_subquery_alias_name | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
There you go, that's exactly the answer.
How about that MAX() query we tried a little while back? | %%sql
SELECT MAX(start_date)
FROM bikeshare
%%sql
EXPLAIN SELECT MAX(start_date)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Let's create another index on start_date to see what the effect on the query plan will be. | %%sql
CREATE INDEX idx_start_date ON bikeshare (start_date)
%%sql
SELECT MAX(start_date)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Same result, but... | %%sql
EXPLAIN SELECT MAX(start_date)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
That's new! In this case it doesn't have to look at any rows, it can just look at one end of the index. We've optimized away the need to even look at the table.
Let's go back to COUNT() and try a few more things before we move on. | %%sql
EXPLAIN SELECT COUNT(*)
FROM bikeshare
%%sql
EXPLAIN SELECT COUNT(start_date)
FROM bikeshare
%%sql
EXPLAIN SELECT COUNT(end_date)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Do you see what happened there?
Normalizing attributes
Let's look at a few tasks you might need to perform if you were normalizing this dataset. Remember that in normalization, we reduce redundancy with the goal of consistency.
What's redundant? Well, the station names for one. | %%sql
SELECT COUNT(DISTINCT start_station)
FROM bikeshare
%%sql
SELECT COUNT(DISTINCT end_station)
FROM bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Hmm, they're different. Let's put them together. | %%sql
SELECT COUNT(DISTINCT station) FROM
(
SELECT start_station AS station FROM bikeshare
UNION
SELECT end_station AS station FROM bikeshare
) a | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
We'll create a table to hold the names of stations. Each station name should be represented once, and we'll assign a primary key to each in the form of a unique integer. | %%sql
CREATE TABLE station (
id SMALLINT NOT NULL AUTO_INCREMENT,
name VARCHAR(100),
PRIMARY KEY (id)
)
%%sql
SELECT COUNT(*)
FROM station | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Looks good. Now we can load the data with an INSERT that draws from our previous query. We can skip specifying the id because MySQL will do that for us.
Note: every database handles this issue its own way. This is a nice convenience in MySQL; other database backends require more work. | %%sql
INSERT INTO station (name)
SELECT DISTINCT station AS name
FROM
(
SELECT start_station AS station FROM bikeshare
UNION
SELECT end_station AS station FROM bikeshare
) a
%%sql
SELECT *
FROM station
LIMIT 10 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
It worked. Now we can update the bikeshare table to add columns for station identifiers. | %%sql
ALTER TABLE bikeshare
ADD COLUMN start_station_id SMALLINT
AFTER start_station | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Looks good. But what exactly just happened? | %%sql
DESCRIBE bikeshare
%%sql
SELECT *
FROM bikeshare
LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
What just happened? Why are all the start_station_id values None?
Let's fill in those values with our new identifiers from the station table. | %%sql
UPDATE bikeshare
INNER JOIN station
ON bikeshare.start_station = station.name
SET bikeshare.start_station_id = station.id
%%sql
SELECT * FROM bikeshare LIMIT 5
%%sql
SELECT * FROM station WHERE id = 161 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Great, now we can drop start_station from bikeshare and save a lot of space. | %%sql
ALTER TABLE bikeshare
DROP COLUMN start_station
%%sql
DESCRIBE bikeshare
%%sql
SELECT * FROM bikeshare LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Worked!
And we can repeat the process for end_station. | %%sql
ALTER TABLE bikeshare
ADD COLUMN end_station_id SMALLINT
AFTER end_station
%%sql
UPDATE bikeshare
INNER JOIN station
ON bikeshare.end_station = station.name
SET bikeshare.end_station_id = station.id
%%sql
ALTER TABLE bikeshare
DROP COLUMN end_station
%%sql
SELECT * FROM bikeshare LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
A lot leaner, right?
JOINs and indexes
Now let's look at queries that return station names, thus requiring a JOIN across the two tables. Keep in mind our two table schema. | %%sql
DESCRIBE station
%%sql
DESCRIBE bikeshare | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Let's try a basic query that looks for the most busy station pairs. | %%sql
SELECT COUNT(*) AS c, start_station_id, end_station_id
FROM bikeshare
GROUP BY start_station_id, end_station_id
ORDER BY c DESC
LIMIT 5 | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Now let's liven it up by joining to station and including station names. We'll need to join twice, using two aliases.
Worked just fine. Let's look under the hood, though. | %%sql
SELECT COUNT(*) AS c, station_1.name AS start_station, station_2.name AS end_station
FROM bikeshare, station AS station_1, station AS station_2
WHERE station_1.id = bikeshare.start_station_id
AND station_2.id = bikeshare.end_station_id
GROUP BY bikeshare.start_station_id, bikeshare.end_station_id
ORDER BY c DES... | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Looks good, and it's in my neighborhood. :)
Let's look at the query plan for all this: | %%sql
EXPLAIN SELECT COUNT(*) AS c, station_1.name AS start_station, station_2.name AS end_station
FROM station AS station_1, station AS station_2, bikeshare
WHERE bikeshare.start_station_id = station_1.id
AND bikeshare.end_station_id = station_2.id
GROUP BY bikeshare.start_station_id, bikeshare.end_station_id
ORDER ... | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Not bad, but it's doing a full table scan on bikeshare. Let's see if some indexes would help with the two joins. | %%sql
CREATE INDEX idx_start_station_id ON bikeshare (start_station_id)
%%sql
CREATE INDEX idx_end_station_id ON bikeshare (end_station_id)
%%sql
EXPLAIN SELECT COUNT(*) AS c, station_1.name AS s1_name, station_2.name AS s2_name
FROM bikeshare, station AS station_1, station AS station_2
WHERE station_1.id = bikeshare... | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Well, it's hard to say how much better this will perform without a lot more data. A COUNT operation simply needs to be able to count everything, if the level of granularity it's counting doesn't already have an easy lookup like we saw before. Sometimes you just don't feel the pain of scale until you hit a scaling thre... | %%sql
CREATE INDEX idx_stations ON bikeshare (start_station_id, end_station_id)
%%sql
EXPLAIN SELECT COUNT(*) AS c, station_1.name AS s1_name, station_2.name AS s2_name
FROM bikeshare, station AS station_1, station AS station_2
WHERE station_1.id = bikeshare.start_station_id
AND station_2.id = bikeshare.end_station_... | lectures/week-07-20151027-more-sql.ipynb | dchud/warehousing-course | cc0-1.0 |
Let's put the CSMF Accuracy calculation right at the top | def measure_prediction_quality(csmf_pred, y_test):
"""Calculate population-level prediction quality (CSMF Accuracy)
Parameters
----------
csmf_pred : pd.Series, predicted distribution of causes
y_test : array-like, labels for test dataset
Results
-------
csmf_acc : float
""... | 2-tutorial-notebook-solutions/4-va_csmf.ipynb | aflaxman/siaman16-va-minitutorial | gpl-3.0 |
How can I test this? | csmf_pred = pd.Series({'cause_1': .5, 'cause_2': .5})
y_test = ['cause_1', 'cause_2']
measure_prediction_quality(csmf_pred, y_test)
csmf_pred = pd.Series({'cause_1': 0., 'cause_2': 1.})
y_test = ['cause_1']*1000 + ['cause_2']
measure_prediction_quality(csmf_pred, y_test) | 2-tutorial-notebook-solutions/4-va_csmf.ipynb | aflaxman/siaman16-va-minitutorial | gpl-3.0 |
Things we don't have time for
An approach to really do the cross-validation out of sample: | val = {}
module = 'Adult'
val[module] = pd.read_csv('../3-data/phmrc_cleaned.csv')
def get_data(module):
X = np.array(val[module].filter(regex='(^s[0-9]+|age|sex)').fillna(0))
y = np.array(val[module].gs_text34)
site = np.array(val[module].site)
return X, y, site
X, y, site = get_data(module)
X.s... | 2-tutorial-notebook-solutions/4-va_csmf.ipynb | aflaxman/siaman16-va-minitutorial | gpl-3.0 |
Introduction
Classical electromagnetism is most often described using maxwell's equations. Instead, we can also describe it using a Lagrange density and an action which is the spacetime integral over the Lagrange density.
The field is represented by a 4-vector in the spacetime-algebra where the first component is the e... | ga = GeometricAlgebra([-1, 1, 1, 1]) | notebooks/em.ipynb | RobinKa/tfga | mit |
Calculate the action
Now we create a function which returns the action $S$ given a field configuration $A(X)$ on a discretized spacetime lattice of size $[N, N, N, N]$. We use the following boundary conditions for $A(X)$:
$A_{t=-1} = 0, A_{t=N} = 0$
$A_{x=-1} = 10 sin(4 * \pi / N * t) e_0, A_{x=N} = -5 e_0$
$A_{y=-1} =... | def get_action(config_a_variable):
# config_a_variable will be of shape [N, N, N, N, 4].
# The last axis' values are the e0, e1, e2, e3 parts of the multivector.
# Finite differences in each direction using padding.
# Example with zero padding (ie. zeros on the boundary):
# 1 2 3
# 1 2 3 0 pa... | notebooks/em.ipynb | RobinKa/tfga | mit |
Initialize the 4-vector field variable randomly | grid_size = [16, 16, 16, 16]
config_a_variable = tf.Variable(tf.random.normal([*grid_size, 4], seed=0)) | notebooks/em.ipynb | RobinKa/tfga | mit |
Optimize the 4-vector field variable to make the action stationary
In order to make the action stationary we use a loss function that is minimal when the action is stationary (ie. the gradient of the action with respect to the field configuration is 0).
We use the mean-squared error to create such a loss function, alth... | optimizer = tf.optimizers.Adam(0.01)
@tf.function
def train_step(config_a_variable):
# Principle of stationary action:
# Minimize the distance of gradient of the action to zero with respect to our field
with tf.GradientTape() as tape_outer:
tape_outer.watch(config_a_variable)
with tf.Gradie... | notebooks/em.ipynb | RobinKa/tfga | mit |
Extract and visualize the optimized electric field
Now we can take the result, that is the $A$ at every spacetime point and visualize it. Obviously we can't visualize a 4 dimensional 4-vector field. However we can look at
individual 2D slices of the electric potential field, which is the first component of the 4-vector... | # Plot electric potential slices. We are not plotting the boundaries here.
plt.figure(figsize=(7, 7))
plt.imshow(config_a_variable[..., 0, 0, 0])
plt.colorbar()
plt.title("Electric potential in TX plane Y=0, Z=0")
plt.xlabel("X")
plt.ylabel("T")
plt.show()
plt.figure(figsize=(7, 7))
plt.imshow(config_a_variable[..., ... | notebooks/em.ipynb | RobinKa/tfga | mit |
In the first figure we can see the potential close to X=0 (where we applied the sine boundary condition) changing over time.
The second figure shows the YZ slice at T=0, X=5 where the potential is almost constant but we still have a radial symmetry.
The last figure shows the XY slice at T=2, Z=0 where the potential tak... | Video("./em_output/electric_potential.webm") | notebooks/em.ipynb | RobinKa/tfga | mit |
Next we can look at the electric vector field corresponding to the electric potential: $E = -\nabla_{x,y,z} \langle A(X) \rangle_{e0} - \nabla_t \langle A(X) \rangle_{e1,e2,e3}$ | def draw_electric_field_xy(t, z):
# Extract XY slice of electric potential [T=t, X, Y, Z=0, 0]
electric_potential = config_a_variable[t, :, :, z, 0]
magnetic_potential_t = config_a_variable[t, :, :, z, 1:]
magnetic_potential_t2 = config_a_variable[t+1, :, :, z, 1:]
# The electric field can be obtai... | notebooks/em.ipynb | RobinKa/tfga | mit |
And again I made a video showing all the time slices. (Direct link: em_output/electric_field.webm) | Video("./em_output/electric_field.webm") | notebooks/em.ipynb | RobinKa/tfga | mit |
Load music data | song_data = graphlab.SFrame('song_data.gl/') | songrecommender/.ipynb_checkpoints/Song recommender-checkpoint.ipynb | anilcs13m/MachineLearning_Mastering | gpl-2.0 |
Explore data
Music data shows how many times a user listened to a song, as well as the details of the song. | song_data.head(5) | songrecommender/.ipynb_checkpoints/Song recommender-checkpoint.ipynb | anilcs13m/MachineLearning_Mastering | gpl-2.0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.