markdown stringlengths 0 1.02M | code stringlengths 0 832k | output stringlengths 0 1.02M | license stringlengths 3 36 | path stringlengths 6 265 | repo_name stringlengths 6 127 |
|---|---|---|---|---|---|
Identifier for storing these features on disk and referring to them later. | feature_list_id = 'tfidf' | _____no_output_____ | MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
Read Data Preprocessed and tokenized questions. | tokens_train = kg.io.load(project.preprocessed_data_dir + 'tokens_lowercase_spellcheck_no_stopwords_train.pickle')
tokens_test = kg.io.load(project.preprocessed_data_dir + 'tokens_lowercase_spellcheck_no_stopwords_test.pickle')
tokens = tokens_train + tokens_test | _____no_output_____ | MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
Extract a set of unique question texts (document corpus). | all_questions_flat = np.array(tokens).ravel()
documents = list(set(' '.join(question) for question in all_questions_flat))
del all_questions_flat | _____no_output_____ | MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
Train TF-IDF vectorizer Create a bag-of-token-unigrams vectorizer. | vectorizer = TfidfVectorizer(
encoding='utf-8',
analyzer='word',
strip_accents='unicode',
ngram_range=(1, 1),
lowercase=True,
norm='l2',
use_idf=True,
smooth_idf=True,
sublinear_tf=True,
)
vectorizer.fit(documents)
model_filename = 'tfidf_vectorizer_{}_ngrams_{}_{}_penalty_{}.pickle'... | _____no_output_____ | MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
Vectorize train and test sets, compute distances | def compute_pair_distances(pair):
q1_doc = ' '.join(pair[0])
q2_doc = ' '.join(pair[1])
pair_dtm = vectorizer.transform([q1_doc, q2_doc])
q1_doc_vec = pair_dtm[0]
q2_doc_vec = pair_dtm[1]
return [
cosine_distances(q1_doc_vec, q2_doc_vec)[0][0],
euclidean_distances(q1_do... | X_train: (404290, 2)
X_test: (2345796, 2)
| MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
Save features | feature_names = [
'tfidf_cosine',
'tfidf_euclidean',
]
project.save_features(X_train, X_test, feature_names, feature_list_id) | _____no_output_____ | MIT | notebooks/feature-tfidf.ipynb | MinuteswithMetrics/kaggle-quora-question-pairs |
PyMC3 Examples GLM Robust Regression with Outlier Detection**A minimal reproducable example of Robust Regression with Outlier Detection using Hogg 2010 Signal vs Noise method.**+ This is a complementary approach to the Student-T robust regression as illustrated in Thomas Wiecki's notebook in the [PyMC3 documentation](... | %matplotlib inline
%qtconsole --colors=linux
import warnings
warnings.filterwarnings('ignore')
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import optimize
import pymc3 as pm
import theano as thno
import theano.tensor as T
# configure some basic options
sns... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Load and Prepare Data We'll use the Hogg 2010 data available at https://github.com/astroML/astroML/blob/master/astroML/datasets/hogg2010test.pyIt's a very small dataset so for convenience, it's hardcoded below | #### cut & pasted directly from the fetch_hogg2010test() function
## identical to the original dataset as hardcoded in the Hogg 2010 paper
dfhogg = pd.DataFrame(np.array([[1, 201, 592, 61, 9, -0.84],
[2, 244, 401, 25, 4, 0.31],
[3, 47, 583, 38, 11, 0.64... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
**Observe**: + Even judging just by eye, you can see these datapoints mostly fall on / around a straight line with positive gradient+ It looks like a few of the datapoints may be outliers from such a line ------ Create Conventional OLS Model The *linear model* is really simple and conventional:$$\bf{y} = \beta^{T} \b... | with pm.Model() as mdl_ols:
## Define weakly informative Normal priors to give Ridge regression
b0 = pm.Normal('b0_intercept', mu=0, sd=100)
b1 = pm.Normal('b1_slope', mu=0, sd=100)
## Define linear model
yest = b0 + b1 * dfhoggs['x']
## Use y error from dataset, convert into theano ... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Sample | with mdl_ols:
## find MAP using Powell, seems to be more robust
start_MAP = pm.find_MAP(fmin=optimize.fmin_powell, disp=True)
## take samples
traces_ols = pm.sample(2000, start=start_MAP, step=pm.NUTS(), progressbar=True) | Optimization terminated successfully.
Current function value: 145.777745
Iterations: 3
Function evaluations: 118
[-----------------100%-----------------] 2000 of 2000 complete in 0.9 sec | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
View Traces**NOTE**: I'll 'burn' the traces to only retain the final 1000 samples | _ = pm.traceplot(traces_ols[-1000:], figsize=(12,len(traces_ols.varnames)*1.5),
lines={k: v['mean'] for k, v in pm.df_summary(traces_ols[-1000:]).iterrows()}) | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
**NOTE:** We'll illustrate this OLS fit and compare to the datapoints in the final plot ------ Create Robust Model: Student-T Method I've added this brief section in order to directly compare the Student-T based method exampled in Thomas Wiecki's notebook in the [PyMC3 documentation](http://pymc-devs.github.io/pymc3/G... | with pm.Model() as mdl_studentt:
## Define weakly informative Normal priors to give Ridge regression
b0 = pm.Normal('b0_intercept', mu=0, sd=100)
b1 = pm.Normal('b1_slope', mu=0, sd=100)
## Define linear model
yest = b0 + b1 * dfhoggs['x']
## Use y error from dataset, convert into th... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Sample | with mdl_studentt:
## find MAP using Powell, seems to be more robust
start_MAP = pm.find_MAP(fmin=optimize.fmin_powell, disp=True)
## two-step sampling to allow Metropolis for nu (which is discrete)
step1 = pm.NUTS([b0, b1])
step2 = pm.Metropolis([nu])
## take samples
traces_studentt ... | Optimization terminated successfully.
Current function value: 107.488021
Iterations: 3
Function evaluations: 77
[-----------------100%-----------------] 2000 of 2000 complete in 1.0 sec | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
View Traces | _ = pm.traceplot(traces_studentt[-1000:]
,figsize=(12,len(traces_studentt.varnames)*1.5)
,lines={k: v['mean'] for k, v in pm.df_summary(traces_studentt[-1000:]).iterrows()}) | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
**Observe:**+ Both parameters `b0` and `b1` show quite a skew to the right, possibly this is the action of a few samples regressing closer to the OLS estimate which is towards the left+ The `nu` parameter seems very happy to stick at `nu = 1`, indicating that a fat-tailed Student-T likelihood has a better fit than a th... | def logp_signoise(yobs, is_outlier, yest_in, sigma_y_in, yest_out, sigma_y_out):
'''
Define custom loglikelihood for inliers vs outliers.
NOTE: in this particular case we don't need to use theano's @as_op
decorator because (as stated by Twiecki in conversation) that's only
required if the likelih... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Sample | with mdl_signoise:
## two-step sampling to create Bernoulli inlier/outlier flags
step1 = pm.NUTS([frac_outliers, yest_out, sigma_y_out, b0, b1])
step2 = pm.BinaryMetropolis([is_outlier], tune_interval=100)
## find MAP using Powell, seems to be more robust
start_MAP = pm.find_MAP(fmin=optimize.fmin... | Optimization terminated successfully.
Current function value: 155.449990
Iterations: 3
Function evaluations: 213
[-----------------100%-----------------] 2000 of 2000 complete in 169.1 sec | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
View Traces | _ = pm.traceplot(traces_signoise[-1000:], figsize=(12,len(traces_signoise.varnames)*1.5),
lines={k: v['mean'] for k, v in pm.df_summary(traces_signoise[-1000:]).iterrows()}) | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
**NOTE:**+ During development I've found that 3 datapoints id=[1,2,3] are always indicated as outliers, but the remaining ordering of datapoints by decreasing outlier-hood is unstable between runs: the posterior surface appears to have a small number of solutions with very similar probability.+ The NUTS sampler seems t... | outlier_melt = pd.melt(pd.DataFrame(traces_signoise['is_outlier', -1000:],
columns=['[{}]'.format(int(d)) for d in dfhoggs.index]),
var_name='datapoint_id', value_name='is_outlier')
ax0 = sns.pointplot(y='datapoint_id', x='is_outlier', data=outlier_melt,
... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
**Observe**:+ The plot above shows the number of samples in the traces in which each datapoint is marked as an outlier, expressed as a percentage.+ In particular, 3 points [1, 2, 3] spend >=95% of their time as outliers+ Contrastingly, points at the other end of the plot close to 0% are our strongest inliers.+ For comp... | cutoff = 5
dfhoggs['outlier'] = np.percentile(traces_signoise[-1000:]['is_outlier'],cutoff, axis=0)
dfhoggs['outlier'].value_counts() | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Posterior Prediction Plots for OLS vs StudentT vs SignalNoise | g = sns.FacetGrid(dfhoggs, size=8, hue='outlier', hue_order=[True,False],
palette='Set1', legend_out=False)
lm = lambda x, samp: samp['b0_intercept'] + samp['b1_slope'] * x
pm.glm.plot_posterior_predictive(traces_ols[-1000:],
eval=np.linspace(-3, 3, 10), lm=lm, samples=200, color='#22CC00', ... | _____no_output_____ | Apache-2.0 | docs/notebooks/GLM-robust-with-outlier-detection.ipynb | ds7788/hello-world |
Sample plots | # load libraries
import os
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline
os.listdir() | _____no_output_____ | MIT | datascience/plots_ds_python_pandas_1.ipynb | futureseadev/hgwxx7 |
sample plot 1 | # load csv
train = pd.read_csv('restaurant-and-market-health-inspections.csv')
train.info()
train.head()
train['grade'].unique()
train.select_dtypes('object')
# plot the count of Unique Values in integer Columns
train.select_dtypes(np.int64).nunique().value_counts().sort_index().plot.bar(color = 'red',
... | _____no_output_____ | MIT | datascience/plots_ds_python_pandas_1.ipynb | futureseadev/hgwxx7 |
sample 2 | # plotting different categories
from collections import OrderedDict
plt.figure(figsize = (20, 16))
plt.style.use('fivethirtyeight')
# Color mapping
colors = OrderedDict({'A': 'red', 'B': 'orange', 'C': 'blue', ' ': 'green'})
mapping = OrderedDict({'A': 'extreme', 'B': 'moderate', 'C': 'vulnerable', ' ': 'non vulnerab... | c:\py37\lib\site-packages\scipy\stats\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different res... | MIT | datascience/plots_ds_python_pandas_1.ipynb | futureseadev/hgwxx7 |
Plot Categoricals | # plot two categorical variables
def plot_categoricals(x, y, data, annotate=False):
"""Plot counts of two categoricals.
Size is raw count for each grouping.
Percentages are for a given value of y."""
# Raw counts
raw_counts = pd.DataFrame(data.groupby(y)[x].value_counts(normalize = False))
... | _____no_output_____ | MIT | datascience/plots_ds_python_pandas_1.ipynb | futureseadev/hgwxx7 |
Value Count Plots | # plot value counts of a column
def plot_value_counts(df, col, condition=False):
"""Plot value counts of a column, optionally with only the heads of a household"""
# apply condition here if required
if condition:
# define condition below <>
df = df.loc[df[col] == condition].copy()
... | _____no_output_____ | MIT | datascience/plots_ds_python_pandas_1.ipynb | futureseadev/hgwxx7 |
Demos: Lecture 4 | import pennylane as qml
import numpy as np | /opt/conda/envs/pennylane/lib/python3.8/site-packages/_distutils_hack/__init__.py:30: UserWarning: Setuptools is replacing distutils.
warnings.warn("Setuptools is replacing distutils.")
| MIT | demos/Lecture04-Demos.ipynb | annabellegrimes/CPEN-400Q |
Demo 1: `qml.ctrl` | def some_function():
qml.PauliX(wires=1)
qml.CNOT(wires=[1, 2])
qml.Hadamard(wires=2)
qml.CRX(0.3, wires=[2, 1])
dev = qml.device('default.qubit', wires=3)
@qml.qnode(dev)
def control_the_thing():
qml.Hadamard(wires=0)
qml.ctrl(some_function, control=0)()
return qml.state()
c... | 0: ──H──╭C──╭C──╭ControlledPhaseShift(1.57)──╭C─────────╭ControlledPhaseShift(1.57)──╭C─────────╭C─────────╭C──╭C──────────╭C──╭C──────────╭┤ State
1: ─────╰X──├C──│────────────────────────────│──────────│────────────────────────────╰RZ(1.57)──╰RY(0.15)──├X──╰RY(-0.15)──├X──╰RZ(-1.57)──├┤ State
2: ─────────╰X──╰Co... | MIT | demos/Lecture04-Demos.ipynb | annabellegrimes/CPEN-400Q |
Demo 2: multi-qubit measurements | dev = qml.device('default.qubit', wires=3)#, shots=10)
@qml.qnode(dev)
def something_parametrized(x, y):
qml.Hadamard(wires=0)
qml.CRX(x, wires=[0, 1])
qml.CRY(y, wires=[1, 2])
return qml.probs(wires=[0])
something_parametrized(0.1, 0.2) | _____no_output_____ | MIT | demos/Lecture04-Demos.ipynb | annabellegrimes/CPEN-400Q |
Demo 3: multi-qubit expectation values | dev = qml.device('default.qubit', wires=3)#, shots=10)
@qml.qnode(dev)
def something_parametrized(x, y):
qml.Hadamard(wires=0)
qml.CRX(x, wires=[0, 1])
qml.CRY(y, wires=[1, 2])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1)), qml.expval(qml.PauliZ(2))
something_parametrized(0.3, 0.4)
d... | _____no_output_____ | MIT | demos/Lecture04-Demos.ipynb | annabellegrimes/CPEN-400Q |
Demo 4: superdense coding | dev = qml.device('default.qubit', wires=2, shots=1)
def create_entangled_state(wires=None):
qml.Hadamard(wires=wires[0])
qml.CNOT(wires=[wires[0], wires[1]])
@qml.qnode(dev)
def superdense_coding(b1=0, b2=0):
create_entangled_state(wires=[0, 1])
if b1 == 1:
qml.PauliZ(wires=0)
... | _____no_output_____ | MIT | demos/Lecture04-Demos.ipynb | annabellegrimes/CPEN-400Q |
1 - Getting Started The main application for `scikit-gstat` is variogram analysis and [Kriging](https://en.wikipedia.org/wiki/Kriging). This Tutorial will guide you through the most basic functionality of `scikit-gstat`. There are other tutorials that will explain specific methods or attributes in `scikit-gstat` in mo... | import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from pprint import pprint
plt.style.use('ggplot') | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
The `Variogram` and `OrdinaryKriging` classes can be loaded directly from `skgstat`. This is the name of the Python module. | from skgstat import Variogram, OrdinaryKriging | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
At the current version, there are some deprecated attributes and method in the `Variogram` class. They do not raise `DeprecationWarning`s, but rather print a warning message to the screen. You can suppress this warning by adding an `SKG_SUPPRESS` environment variable | %set_env SKG_SUPPRESS=true | env: SKG_SUPPRESS=true
| MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
1.1 Load data You can find a prepared example data set in the `./data` subdirectory. This example is extracted from a generated Gaussian random field. We can expect the field to be stationary and show a nice spatial dependence, because it was created that way.We can load one of the examples and have a look at the data... | data = pd.read_csv('./data/sample_sr.csv')
print("Loaded %d rows and %d columns" % data.shape)
data.head() | Loaded 200 rows and 3 columns
| MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
Get a first overview of your data by plotting the `x` and `y` coordinates and visually inspect how the `z` spread out. | fig, ax = plt.subplots(1, 1, figsize=(9, 9))
art = ax.scatter(data.x,data.y, s=50, c=data.z, cmap='plasma')
plt.colorbar(art); | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
We can already see a lot from here: * The small values seem to concentrate on the upper left and lower right corner* Larger values are arranged like a band from lower left to upper right corner* To me, each of these blobs seem to have a diameter of something like 30 or 40 units.* The distance between the minimum and ma... | V = Variogram(data[['x', 'y']].values, data.z.values, normalize=False, maxlag=60, n_lags=15)
fig = V.plot(show=False) | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
The upper subplot show the histogram for the count of point-pairs in each lag class. You can see various things here:* As expected, there is a clear spatial dependency, because semi-variance increases with distance (blue dots)* The default `spherical` variogram model is well fitted to the experimental data* The shape o... | print('Sample variance: %.2f Variogram sill: %.2f' % (data.z.var(), V.describe()['sill'])) | Sample variance: 1.10 Variogram sill: 1.26
| MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
The `describe` method will return the most important parameters as a dictionary. And we can simply print the variogram ob,ect to the screen, to see all parameters. | pprint(V.describe())
print(V) | spherical Variogram
-------------------
Estimator: matheron
Effective Range: 39.50
Sill: 1.26
Nugget: 0.00
| MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
1.3 Kriging The Kriging class will now use the Variogram from above to estimate the Kriging weights for each grid cell. This is done by solving a linear equation system. For an unobserved location $s_0$, we can use the distances to 5 observation points and build the system like:$$\begin{pmatrix}\gamma(s_1, s_1) & \gam... | ok = OrdinaryKriging(V, min_points=5, max_points=15, mode='exact') | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
The `transform` method will apply the interpolation for passed arrays of coordinates. It requires each dimension as a single 1D array. We can easily build a meshgrid of 100x100 coordinates and pass them to the interpolator. To recieve a 2D result, we can simply reshape the result. The Kriging error will be available as... | # build the target grid
xx, yy = np.mgrid[0:99:100j, 0:99:100j]
field = ok.transform(xx.flatten(), yy.flatten()).reshape(xx.shape)
s2 = ok.sigma.reshape(xx.shape) | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
And finally, we can plot the result. | fig, axes = plt.subplots(1, 2, figsize=(16, 8))
art = axes[0].matshow(field.T, origin='lower', cmap='plasma')
axes[0].set_title('Interpolation')
axes[0].plot(data.x, data.y, '+k')
axes[0].set_xlim((0,100))
axes[0].set_ylim((0,100))
plt.colorbar(art, ax=axes[0])
art = axes[1].matshow(s2.T, origin='lower', cmap='YlGn_r'... | _____no_output_____ | MIT | docs/tutorials/01_getting_started.ipynb | rhugonnet/scikit-gstat |
KNN | import pickle
import numpy as np
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.metrics import classification_report, confusion_matrix
from sklearn.model_selection import GridSearchCV
from sklearn.model_selection import StratifiedSh... | {'n_neighbors': 5}
[[6164 75 373 345 0]
[ 71 6402 356 352 0]
[ 351 360 8975 105 0]
[ 368 397 123 8683 0]
[ 5 5 7 25 1]]
precision recall f1-score support
0 0.89 0.89 0.89 6957
1 0.88 0.89 0.89 71... | MIT | MLGame/games/snake/ml/train.py.ipynb | Liuian/1092_INTRODUCTION-TO-MACHINE-LEARNING-AND-ITS-APPLICATION-TO-GAMING |
Bayesian Regression Using NumPyroIn this tutorial, we will explore how to do bayesian regression in NumPyro, using a simple example adapted from Statistical Rethinking [[1](References)]. In particular, we would like to explore the following: - Write a simple model using the `sample` NumPyro primitive. - Run inference ... | %reset -s -f
import jax
import jax.numpy as np
from jax import random, vmap
from jax.config import config; config.update("jax_platform_name", "cpu")
from jax.scipy.special import logsumexp
import matplotlib
import matplotlib.pyplot as plt
import numpy as onp
import pandas as pd
import seaborn as sns
from numpyro.diagn... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
DatasetFor this example, we will use the `WaffleDivorce` dataset from Chapter 05, Statistical Rethinking [[1](References)]. The dataset contains divorce rates in each of the 50 states in the USA, along with predictors such as population, median age of marriage, whether it is a Southern state and, curiously, number of ... | DATASET_URL = 'https://raw.githubusercontent.com/rmcelreath/rethinking/master/data/WaffleDivorce.csv'
dset = pd.read_csv(DATASET_URL, sep=';')
dset | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Let us plot the pair-wise relationship amongst the main variables in the dataset, using `seaborn.pairplot`. | vars = ['Population', 'MedianAgeMarriage', 'Marriage', 'WaffleHouses', 'South', 'Divorce']
sns.pairplot(dset, x_vars=vars, y_vars=vars, palette='husl'); | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
From the plots above, we can clearly observe that there is a relationship between divorce rates and marriage rates in a state (as might be expected), and also between divorce rates and median age of marriage. There is also a weak relationship between number of Waffle Houses and divorce rates, which is not obvious from ... | sns.regplot('WaffleHouses', 'Divorce', dset); | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Regression Model to Predict Divorce RateLet us now write a regressionn model in *NumPyro* to predict the divorce rate as a linear function of marriage rate and median age of marriage in each of the states. First, note that our predictor variables have somewhat different scales. It is a good practice to standardize our... | dset['AgeScaled'] = (dset.MedianAgeMarriage - onp.mean(dset.MedianAgeMarriage)) / onp.std(dset.MedianAgeMarriage)
dset['MarriageScaled'] = (dset.Marriage - onp.mean(dset.Marriage)) / onp.std(dset.Marriage)
dset['DivorceScaled'] = (dset.Divorce - onp.mean(dset.Divorce)) / onp.std(dset.Divorce) | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
We write the NumPyro model as follows. While the code should largely be self-explanatory, take note of the following: - In NumPyro, model code is any Python callable that can accept arguments and keywords. For HMC which we will be using for this tutorial, these arguments and keywords cannot change during model executio... | def model(marriage=None, age=None, divorce=None):
a = sample('a', dist.Normal(0., 0.2))
M, A = 0., 0.
if marriage is not None:
bM = sample('bM', dist.Normal(0., 0.5))
M = bM * marriage
if age is not None:
bA = sample('bA', dist.Normal(0., 0.5))
A = bA * age
sigma = sa... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Model 1: Predictor - Marriage RateWe first try to model the divorce rate as depending on a single variable, marriage rate. As mentioned above, we can use the same `model` code as earlier, but only pass values for `marriage` and `divorce` keyword arguments. We will use the No U-Turn Sampler (see [[5](References)] for m... | # Start from this source of randomness. We will split keys for subsequent operations.
rng = random.PRNGKey(0)
rng_, rng = random.split(rng)
# Initialize the model.
init_params, potential_fn, constrain_fn = initialize_model(rng_, model,
marriage=dset.MarriageS... | warmup: 100%|██████████| 1000/1000 [00:12<00:00, 78.24it/s, 1 steps of size 6.99e-01. acc. prob=0.79]
sample: 100%|██████████| 2000/2000 [00:03<00:00, 515.37it/s, 3 steps of size 6.99e-01. acc. prob=0.88]
| MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Posterior Distribution over the Regression ParametersWe notice that the progress bar gives us online statistics on the acceptance probability, step size and number of steps taken per sample while running NUTS. In particular, during warmup, we adapt the step size and mass matrix to achieve a certain target acceptance p... | def plot_regression(x, y_mean, y_hpdi):
# Sort values for plotting by x axis
idx = np.argsort(x)
marriage = x[idx]
mean = y_mean[idx]
hpdi = y_hpdi[:, idx]
divorce = dset.DivorceScaled.values[idx]
# Plot
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(6, 6))
ax.plot(marriage, mean... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Posterior Predictive DistributionLet us now look at the posterior predictive distribution to see how our predictive distribution looks with respect to the observed divorce rates. To get samples from the posterior predictive distribution, we need to run the model by substituting the latent parameters with samples from ... | def predict(rng, post_samples, model, *args, **kwargs):
model = substitute(seed(model, rng), post_samples)
model_trace = trace(model).get_trace(*args, **kwargs)
return model_trace['obs']['value']
# vectorize predictions via vmap
predict_fn = vmap(lambda rng, samples: predict(rng, samples, model, marriage=ds... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
We will use the same `plot_regression` function as earlier. We notice that our CI for the predictive distribution is much broader as compared to the last plot due to the additional noise introduced by the `sigma` parameter. Note that most data points lie well within the 90% CI, which indicates a good fit. Model Log Lik... | def log_lk(rng, params, model, *args, **kwargs):
model = substitute(seed(model, rng), params)
model_trace = trace(model).get_trace(*args, **kwargs)
obs_node = model_trace['obs']
return np.sum(obs_node['fn'].log_prob(obs_node['value']))
def expected_log_likelihood(rng, params, model, *args, **kwargs... | Log likelihood: -68.14618682861328
| MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Model 2: Predictor - Median Age of MarriageWe will now model the divorce rate as a function of the median age of marriage. The computations are mostly a reproduction of what we did for Model 1. Notice the following: - Divorce rate is inversely related to the age of marriage. Hence states where the median age of marria... | rng, rng_ = random.split(rng)
init_params, potential_fn, constrain_fn = initialize_model(rng_, model,
age=dset.AgeScaled.values,
divorce=dset.DivorceScaled.values)
samples_2 = mcmc(num_warmup, num_sa... | Log likelihood: -60.926387786865234
| MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Model 3: Predictor - Marriage Rate and Median Age of MarriageFinally, we will also model divorce rate as depending on both marriage rate as well as the median age of marriage. Note that there is no increase in the model's log likelihood over Model 2 which likely indicates that the marginal information from marriage ra... | rng, rng_ = random.split(rng)
init_params, potential_fn, constrain_fn = initialize_model(rng_, model,
marriage=dset.MarriageScaled.values,
age=dset.AgeScaled.values,
... | Log likelihood: -61.04328918457031
| MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Divorce Rate Residuals by StateThe regression plots above shows that the observed divorce rates for many states differs considerably from the mean regression line. To dig deeper into how the last model (Model 3) under-predicts or over-predicts for each of the states, we will plot the posterior predictive and residuals... | # Predictions for Model 3.
rng, rng_ = random.split(rng)
predict_fn = vmap(lambda rng, samples: predict(rng, samples, model,
marriage=dset.MarriageScaled.values,
age=dset.AgeScaled.values))
predictions_3 = predict_fn(random.sp... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
The plot on the left shows the mean predictions with 90% CI for each of the states using Model 3. The gray markers indicate the actual observed divorce rates. The right plot shows the residuals for each of the states, and both these plots are sorted by the residuals, i.e. at the bottom, we are looking at states where t... | def model_se(marriage, age, divorce_sd, divorce=None):
a = sample('a', dist.Normal(0., 0.2))
bM = sample('bM', dist.Normal(0., 0.5))
M = bM * marriage
bA = sample('bA', dist.Normal(0., 0.5))
A = bA * age
sigma = sample('sigma', dist.Exponential(1.))
mu = a + M + A
divorce_rate = sample('... | warmup: 100%|██████████| 1000/1000 [00:19<00:00, 50.19it/s, 15 steps of size 2.16e-01. acc. prob=0.89]
sample: 100%|██████████| 3000/3000 [00:06<00:00, 442.19it/s, 15 steps of size 2.16e-01. acc. prob=0.94]
| MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Effect of Incorporating Measurement Noise on ResidualsNotice that our values for the regression coefficients is very similar to Model 3. However, introducing measurement noise allows us to more closely match our predictive distributions to the observed values. We can see this if we plot the residuals as earlier. | rng, rng_ = random.split(rng)
predict_fn = vmap(lambda rng, samples: predict(rng, samples, model_se,
marriage=dset.MarriageScaled.values,
age=dset.AgeScaled.values,
divorce_sd=ds... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
The plot above shows the residuals for each of the states, along with the measurement noise given by inner error bar. The gray dots are the mean residuals from our earlier Model 3. Notice how having an additional degree of freedom to model the measurement noise has shrunk the residuals. In particular, for Idaho and Mai... | fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6))
x = dset.DivorceScaledSD.values
y1 = np.mean(residuals_3, 0)
y2 = np.mean(residuals_4, 0)
ax.plot(x, y1, ls='none', marker='o')
ax.plot(x, y2, ls='none', marker='o')
for i, (j, k) in enumerate(zip(y1, y2)):
ax.plot([x[i], x[i]], [j, k], '--', color='gray');... | _____no_output_____ | MIT | notebooks/source/bayesian_regression.ipynb | Anthonymcqueen21/numpyro |
Mutation analysis1. Calculate the mutation rate (number of mutations/number of unique sequences) 2. Consider only the sequences between 2000 and 20203. Write the different files (Year : Mutation rate) | from google.colab import drive
drive.mount('/content/gdrive')
%cd 'gdrive/MyDrive/Machine Learning/coronavirus/analysis'
!ls
import os
import pandas as pd
import numpy as np
#List all the directory names
dir_name = os.listdir('./H1N_H9N')
for name in dir_name:
df = pd.read_csv('./H1N_H9N/' + name)
#Select only se... | _____no_output_____ | MIT | analysis/Mutation_analysis.ipynb | chuducthang77/coronavirus |
Table of Contents 0.0.1 Cover Slide 10.0.2 Cover Slide 21 Headline Slide2 Preprocessing3 Headline Subslide4 Fragment4.0.1 Divider5 Markdown Examples5.0.0.1 Text6 Headline Subslide6.0.0.1 Code7 ... | # Add all necessary imports here
import matplotlib.pyplot as plt
%matplotlib inline
plt.style.reload_library()
plt.style.use("ggplot") | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
Cover Slide 1 | <image>
<section data-background="img/cover.jpg" data-state="img-transparent no-title-footer">
<div class="intro-body">
<div class="intro_h1"><h1>Title</h1></div>
<h3>Subtitle of the Presentation</h3>
<p><strong><span class="a">Speaker 1</span></strong> <span class="b"></span> <span>Job Title</span></p>
<p><strong><spa... | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
Cover Slide 2 | <image>
<section data-state="no-title-footer">
<div class="intro_h1"><h1>Title</h1></div>
<h3>Subtitle of the Presentation</h3>
<p><strong><span class="a">Speaker 1</span></strong> <span class="b"></span> <span>Job Title</span></p>
<p><strong><span class="a">Speaker 2</span></strong> <span class="b"></span> <span>Job T... | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
Headline Slide Preprocessing       | def f(x):
"""a docstring"""
return x**2 | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
Headline Subslide | plt.plot([1,2,3,4])
plt.ylabel('some numbers')
plt.show() | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
FragmentPress the right arrow. - I am a Fragement - I am another one Divider | <image>
</section>
<section data-background="#F27C3A" data-state="no-title-footer">
<div class="divider_h1">
<h1>Divider</h1>
</div>
</section>
</image> | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
Markdown Examples TextIt's very easy to make some words **bold** and other words *italic* with Markdown. You can even [link to Google!](http://google.com) Headline Subslide Code```javascriptvar s = "JavaScript syntax highlighting";alert(s);``` ```pythons = "Python syntax highlighting"print s``` ```No language indicat... | <image>
</section>
<section data-background="#0093C9" data-state="no-title-footer">
<div class="divider_h1">
<h1>Questions???</h1>
</div>
</section>
</image> | _____no_output_____ | MIT | reports/Presentations/Presentation_241117/timing_presentation.ipynb | EstevaoVieira/spikelearn |
test: 30% train-val 70%To simulate noisy label acquisition, assume a labeler quality p. then use a random we first hide the labels of all examples for each dataset. At the point in an experiment when a label is acquired, we generate a label according to the labeler quality p: we assign the example's original label with... | %reload_ext autoreload
%autoreload 2
import sys, os, wget
sys.path.append('../../')
import pandas as pd
import numpy as np
import load_data
import ipywidgets
from IPython.display import display
args = {'options': ['read', 'download'],
'label': 'read',
'description': 'mode:' ,
... | _____no_output_____ | Apache-2.0 | examples_artin/applied_to_other_datasets.ipynb | artinmajdi/crowd-kit |
guide for ipywidgetssource: | widgets.FloatRangeSlider(
value=[5, 7.5],
min=0,
max=10.0,
step=0.1,
description='Test:',
disabled=False,
continuous_update=False,
orientation='horizontal',
readout=True,
readout_format='.1f',
)
b = widgets.BoundedFloatText(
value=7.5,
min=0,
max=10.0,
step=0.1,
... | _____no_output_____ | Apache-2.0 | examples_artin/applied_to_other_datasets.ipynb | artinmajdi/crowd-kit |
XGBoost Cloud Prediction - Iris ClassificationInvoke SageMaker Prediction Service | # Acquire a realtime endpoint
endpoint_name = 'xgboost-iris-v1'
predictor = sagemaker.predictor.Predictor (endpoint_name=endpoint_name)
predictor.serializer = CSVSerializer()
# Test predictive quality against data in validation file
df_all = pd.read_csv('iris_validation.csv',
names=['encoded_class'... | _____no_output_____ | Apache-2.0 | 5 Xgboost/IrisClassification/xgboost_cloud_prediction_template.ipynb | jaypeeml/AWSSagemaker |
宣告- 只能存不重複的元素- 因為是無序的，所以每次編譯後的順序都會不同 | a = {1, 2, 3, 2, 4, 5, 2}
b = set([1, 2, 3, 2, 4, 5, 2])
print(a, type(a))
print(b, type(b))
s1.add(5)
print(s1)
s1.add(5)
print(s1)
s1.remove(5)
print(s1)
# 因為找不到，所以會報錯
#s1.remove(8)
#print(s1)
a = '1234512'
print(set(a))
s1 = {1, 2, 3, 4}
s2 = {3, 4, 5, 6}
print('交集:', s1 & s2)
print('聯集:', s1 | s2)
print('對稱差集:',... | 交集: {3, 4}
聯集: {1, 2, 3, 4, 5, 6}
對稱差集: {1, 2, 5, 6}
差集1: {1, 2}
差集2: {5, 6}
| MIT | Python/[Python] Set.ipynb | ZongSingHuang/Data-Scientist-Tokyo |
Image annotations for a batch of samplesUsing this notebook, cardiologists are able to quickly view and annotate MRI images for a batch of samples. These annotated images become the training data for the next round of modeling. Setup This notebook assumes Terra is running custom Docker image ghcr.io/bro... | # TODO(deflaux): remove this cell after gcr.io/broad-ml4cvd/deeplearning:tf2-latest-gpu has this preinstalled.
from ml4h.runtime_data_defines import determine_runtime
from ml4h.runtime_data_defines import Runtime
if Runtime.ML4H_VM == determine_runtime():
!pip3 install --user ipycanvas==0.7.0 ipyannotations==0.2.1
... | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
Define the batch of samples to annotate Edit the CSV file path below, if needed, to either a local file or one in Cloud Storage. | #---[ EDIT AND RUN THIS CELL TO READ FROM A LOCAL FILE OR A FILE IN CLOUD STORAGE ]---
SAMPLE_BATCH_FILE = None
if SAMPLE_BATCH_FILE:
samples_df = pd.read_csv(tf.io.gfile.GFile(SAMPLE_BATCH_FILE))
else:
# Normally these would all be the same or similar TMAP. We are using different ones here just to make it
# mor... | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
Annotate the batch! Annotate with pointsUse points to annotate landmarks within the images. | # Note: a zoom level of 1.0 displays the tensor as-is. For higher zoom levels, this code currently
# use the PIL library to scale the image.
annotator = BatchImageAnnotator(samples=samples_df,
zoom=2.0,
annotation_categories=['region_of_interest'],
... | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
Annotate with polygonsUse polygons to annotate arbitrarily shaped regions within the images. | # Note: a zoom level of 1.0 displays the tensor as-is. For higher zoom levels, this code currently
# use the PIL library to scale the image.
annotator = BatchImageAnnotator(samples=samples_df,
zoom=2.0,
annotation_categories=['region_of_interest'],
... | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
Annotate with rectanglesUse rectangles to annotate rectangular regions within the image. | # Note: a zoom level of 1.0 displays the tensor as-is. For higher zoom levels, this code currently
# use the PIL library to scale the image.
annotator = BatchImageAnnotator(samples=samples_df,
zoom=2.0,
annotation_categories=['region_of_interest'],
... | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
View the stored annotations | annotator.view_recent_submissions(count=10) | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
Provenance | import datetime
print(datetime.datetime.now())
%%bash
pip3 freeze | _____no_output_____ | BSD-3-Clause | notebooks/review_results/image_annotations.ipynb | deflaux/ml4h |
'ewm' series is the most stationary out of all the series. Hence we model on 'ewm' | from pandas.tools.plotting import autocorrelation_plot
autocorrelation_plot(ewm)
from statsmodels.tsa.arima_model import ARIMA
model = ARIMA(ewm, order = (15, 1, 0))
model_fit = model.fit(disp = 0)
plt.plot(model_fit.fittedvalues)
logpred_diff = pd.Series(model_fit.fittedvalues, index = ewm.index)
logpred_cumsum = logp... | _____no_output_____ | MIT | Gun Violence.ipynb | itsmepiyush2/Effects-of-Gun-Violence-forecast |
Testing the functionalities of MetaTuner on bcancer dataset | from mango import MetaTuner
# Define different classifiers
from scipy.stats import uniform
from sklearn import datasets
from sklearn.neighbors import KNeighborsClassifier
from sklearn.model_selection import cross_val_score
data = datasets.load_breast_cancer()
X = data.data
Y = data.target | _____no_output_____ | Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
XGBoost | from xgboost import XGBClassifier
param_dict_xgboost = {"learning_rate": uniform(0, 1),
"gamma": uniform(0, 5),
"max_depth": range(1, 16),
"n_estimators": range(1, 4),
"booster":['gbtree','gblinear','dart']
}
X_xgboost = X
Y_xgboost = Y
# import... | _____no_output_____ | Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
KNN | param_dict_knn = {"n_neighbors": range(1, 101),
'algorithm' : ['auto', 'ball_tree', 'kd_tree', 'brute']
}
X_knn = X
Y_knn = Y
def objective_knn(args_list):
global X_knn,Y_knn
results = []
for hyper_par in args_list:
clf = KNeighborsClassifier()
clf.s... | _____no_output_____ | Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
SVM | from mango.domain.distribution import loguniform
from sklearn import svm
param_dict_svm = {"gamma": uniform(0.1, 4),
"C": loguniform(-7, 10)}
X_svm = X
Y_svm = Y
def objective_svm(args_list):
global X_svm,Y_svm
#print('SVM:',args_list)
results = []
for hyper_par in args_list:
... | _____no_output_____ | Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
Decision Tree | from sklearn.tree import DecisionTreeClassifier
param_dict_dtree = {
"max_features": ['auto', 'sqrt', 'log2'],
"max_depth": range(1,21),
"splitter":['best','random'],
"criterion":['gini','entropy']
}
X_dtree = X
Y_dtree = Y
print(X_dtree.... | [0.9016522788452613, 0.9016244314489928, 0.6264204028589994, 0.6274204028589994, 0.924412884062007, 0.924403601596584, 0.9208948296667595, 0.9402394876079088, 0.91914972616727, 0.8700083542188805, 0.9208948296667595, 0.8893158822983386, 0.9384665367121507, 0.8752900770444629, 0.7431913116123643, 0.924403601596584, 0.88... | Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
A simple chart of function evaluations | def count_elements(seq):
"""Tally elements from `seq`."""
hist = {}
for i in seq:
hist[i] = hist.get(i, 0) + 1
return hist
def ascii_histogram(seq):
"""A horizontal frequency-table/histogram plot."""
counted = count_elements(seq)
for k in sorted(counted):
print('{0:5d} {1}'.... | 0 ++++
1 +++
2 ++++++++++++
3 +++++++++
| Apache-2.0 | benchmarking/MetaTuner_Examples/MetaTuner-on-bcancer.ipynb | jashanmeet-collab/mango |
May be possible to entangle all ions with global pulse with multiple tones. | from numpy import *
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
from Error_dist import func_str
# 10-ion test
N = 11
x = arange(1, N)
y = x
def func(x, a, b, c, d, e):
return (a / x ** 0.5 + b / x ** 0.7 + c / x ** 1 + d / x ** 1.5 + e / x ** 2)
# Assume entangling strengt\ scales as 1 ... | _____no_output_____ | Apache-2.0 | Global beam test.ipynb | jlfly12/qrsim |
**4장 – 모델 훈련** _이 노트북은 4장에 있는 모든 샘플 코드와 연습문제 해답을 가지고 있습니다._ 구글 코랩에서 실행하기 설정 먼저 몇 개의 모듈을 임포트합니다. 맷플롯립 그래프를 인라인으로 출력하도록 만들고 그림을 저장하는 함수를 준비합니다. 또한 파이썬 버전이 3.5 이상인지 확인합니다(파이썬 2.x에서도 동작하지만 곧 지원이 중단되므로 파이썬 3을 사용하는 것이 좋습니다). 사이킷런 버전이 0.20 이상인지도 확인합니다. | # 파이썬 ≥3.5 필수
import sys
assert sys.version_info >= (3, 5)
# 사이킷런 ≥0.20 필수
import sklearn
assert sklearn.__version__ >= "0.20"
# 공통 모듈 임포트
import numpy as np
import os
# 노트북 실행 결과를 동일하게 유지하기 위해
np.random.seed(42)
# 깔끔한 그래프 출력을 위해
%matplotlib inline
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rc('ax... | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
선형 회귀 | import numpy as np
X = 2 * np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)
plt.plot(X, y, "b.")
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.axis([0, 2, 0, 15])
save_fig("generated_data_plot")
plt.show() | 그림 저장: generated_data_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
**식 4-4: 정규 방정식**$\hat{\boldsymbol{\theta}} = (\mathbf{X}^T \mathbf{X})^{-1} \mathbf{X}^T \mathbf{y}$ | X_b = np.c_[np.ones((100, 1)), X] # 모든 샘플에 x0 = 1을 추가합니다.
theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)
theta_best | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
$\hat{y} = \mathbf{X} \boldsymbol{\hat{\theta}}$ | X_new = np.array([[0], [2]])
X_new_b = np.c_[np.ones((2, 1)), X_new] # 모든 샘플에 x0 = 1을 추가합니다.
y_predict = X_new_b.dot(theta_best)
y_predict
plt.plot(X_new, y_predict, "r-")
plt.plot(X, y, "b.")
plt.axis([0, 2, 0, 15])
plt.show() | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
책에 있는 그림은 범례와 축 레이블이 있는 그래프입니다: | plt.plot(X_new, y_predict, "r-", linewidth=2, label="Predictions")
plt.plot(X, y, "b.")
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.legend(loc="upper left", fontsize=14)
plt.axis([0, 2, 0, 15])
save_fig("linear_model_predictions_plot")
plt.show()
from sklearn.linear_model import Line... | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
`LinearRegression` 클래스는 `scipy.linalg.lstsq()` 함수("least squares"의 약자)를 사용하므로 이 함수를 직접 사용할 수 있습니다: | # 싸이파이 lstsq() 함수를 사용하려면 scipy.linalg.lstsq(X_b, y)와 같이 씁니다.
theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)
theta_best_svd | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
이 함수는 $\mathbf{X}^+\mathbf{y}$을 계산합니다. $\mathbf{X}^{+}$는 $\mathbf{X}$의 _유사역행렬_ (pseudoinverse)입니다(Moore–Penrose 유사역행렬입니다). `np.linalg.pinv()`을 사용해서 유사역행렬을 직접 계산할 수 있습니다: $\boldsymbol{\hat{\theta}} = \mathbf{X}^{-1}\hat{y}$ | np.linalg.pinv(X_b).dot(y) | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
경사 하강법 배치 경사 하강법 **식 4-6: 비용 함수의 그레이디언트 벡터**$\dfrac{\partial}{\partial \boldsymbol{\theta}} \text{MSE}(\boldsymbol{\theta}) = \dfrac{2}{m} \mathbf{X}^T (\mathbf{X} \boldsymbol{\theta} - \mathbf{y})$**식 4-7: 경사 하강법의 스텝**$\boldsymbol{\theta}^{(\text{next step})} = \boldsymbol{\theta} - \eta \dfrac{\partial}{\partial \bo... | eta = 0.1 # 학습률
n_iterations = 1000
m = 100
theta = np.random.randn(2,1) # 랜덤 초기화
for iteration in range(n_iterations):
gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)
theta = theta - eta * gradients
theta
X_new_b.dot(theta)
theta_path_bgd = []
def plot_gradient_descent(theta, eta, theta_path=None):
m ... | 그림 저장: gradient_descent_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
확률적 경사 하강법 | theta_path_sgd = []
m = len(X_b)
np.random.seed(42)
n_epochs = 50
t0, t1 = 5, 50 # 학습 스케줄 하이퍼파라미터
def learning_schedule(t):
return t0 / (t + t1)
theta = np.random.randn(2,1) # 랜덤 초기화
for epoch in range(n_epochs):
for i in range(m):
if epoch == 0 and i < 20: # 책에는 없음
y... | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
미니배치 경사 하강법 | theta_path_mgd = []
n_iterations = 50
minibatch_size = 20
np.random.seed(42)
theta = np.random.randn(2,1) # 랜덤 초기화
t0, t1 = 200, 1000
def learning_schedule(t):
return t0 / (t + t1)
t = 0
for epoch in range(n_iterations):
shuffled_indices = np.random.permutation(m)
X_b_shuffled = X_b[shuffled_indices]
... | 그림 저장: gradient_descent_paths_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
다항 회귀 | import numpy as np
import numpy.random as rnd
np.random.seed(42)
m = 100
X = 6 * np.random.rand(m, 1) - 3
y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)
plt.plot(X, y, "b.")
plt.xlabel("$x_1$", fontsize=18)
plt.ylabel("$y$", rotation=0, fontsize=18)
plt.axis([-3, 3, 0, 10])
save_fig("quadratic_data_plot")
plt.show()
f... | 그림 저장: high_degree_polynomials_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
학습 곡선 | from sklearn.metrics import mean_squared_error
from sklearn.model_selection import train_test_split
def plot_learning_curves(model, X, y):
X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)
train_errors, val_errors = [], []
for m in range(1, len(X_train) + 1):
m... | 그림 저장: learning_curves_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
규제가 있는 선형 모델 릿지 회귀 | np.random.seed(42)
m = 20
X = 3 * np.random.rand(m, 1)
y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5
X_new = np.linspace(0, 3, 100).reshape(100, 1) | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
**식 4-8: 릿지 회귀의 비용 함수**$J(\boldsymbol{\theta}) = \text{MSE}(\boldsymbol{\theta}) + \alpha \dfrac{1}{2}\sum\limits_{i=1}^{n}{\theta_i}^2$ | from sklearn.linear_model import Ridge
ridge_reg = Ridge(alpha=1, solver="cholesky", random_state=42)
ridge_reg.fit(X, y)
ridge_reg.predict([[1.5]])
ridge_reg = Ridge(alpha=1, solver="sag", random_state=42)
ridge_reg.fit(X, y)
ridge_reg.predict([[1.5]])
from sklearn.linear_model import Ridge
def plot_model(model_class... | 그림 저장: ridge_regression_plot
| Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
**노트**: 향후 버전이 바뀌더라도 동일한 결과를 만들기 위해 사이킷런 0.21 버전의 기본값인 `max_iter=1000`과 `tol=1e-3`으로 지정합니다. | sgd_reg = SGDRegressor(penalty="l2", max_iter=1000, tol=1e-3, random_state=42)
sgd_reg.fit(X, y.ravel())
sgd_reg.predict([[1.5]]) | _____no_output_____ | Apache-2.0 | 04_training_linear_models.ipynb | probationer070/handson-ml2 |
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