# Titan Robotics Team 2022: Data Analysis Module
# Written by Arthur Lu & Jacob Levine
# Notes:
# this should be imported as a python module using 'import analysis'
# this should be included in the local directory or environment variable
# this module has been optimized for multhreaded computing
# current benchmark of optimization: 1.33 times faster
# setup:
__version__ = "1.1.13.009"
# changelog should be viewed using print(analysis.__changelog__)
__changelog__ = """changelog:
1.1.13.009:
- moved elo, glicko2, trueskill functions under class Metrics
1.1.13.008:
- moved Glicko2 to a seperate package
1.1.13.007:
- fixed bug with trueskill
1.1.13.006:
- cleaned up imports
1.1.13.005:
- cleaned up package
1.1.13.004:
- small fixes to regression to improve performance
1.1.13.003:
- filtered nans from regression
1.1.13.002:
- removed torch requirement, and moved Regression back to regression.py
1.1.13.001:
- bug fix with linear regression not returning a proper value
- cleaned up regression
- fixed bug with polynomial regressions
1.1.13.000:
- fixed all regressions to now properly work
1.1.12.006:
- fixed bg with a division by zero in histo_analysis
1.1.12.005:
- fixed numba issues by removing numba from elo, glicko2 and trueskill
1.1.12.004:
- renamed gliko to glicko
1.1.12.003:
- removed depreciated code
1.1.12.002:
- removed team first time trueskill instantiation in favor of integration in superscript.py
1.1.12.001:
- improved readibility of regression outputs by stripping tensor data
- used map with lambda to acheive the improved readibility
- lost numba jit support with regression, and generated_jit hangs at execution
- TODO: reimplement correct numba integration in regression
1.1.12.000:
- temporarily fixed polynomial regressions by using sklearn's PolynomialFeatures
1.1.11.010:
- alphabeticaly ordered import lists
1.1.11.009:
- bug fixes
1.1.11.008:
- bug fixes
1.1.11.007:
- bug fixes
1.1.11.006:
- tested min and max
- bug fixes
1.1.11.005:
- added min and max in basic_stats
1.1.11.004:
- bug fixes
1.1.11.003:
- bug fixes
1.1.11.002:
- consolidated metrics
- fixed __all__
1.1.11.001:
- added test/train split to RandomForestClassifier and RandomForestRegressor
1.1.11.000:
- added RandomForestClassifier and RandomForestRegressor
- note: untested
1.1.10.000:
- added numba.jit to remaining functions
1.1.9.002:
- kernelized PCA and KNN
1.1.9.001:
- fixed bugs with SVM and NaiveBayes
1.1.9.000:
- added SVM class, subclasses, and functions
- note: untested
1.1.8.000:
- added NaiveBayes classification engine
- note: untested
1.1.7.000:
- added knn()
- added confusion matrix to decisiontree()
1.1.6.002:
- changed layout of __changelog to be vscode friendly
1.1.6.001:
- added additional hyperparameters to decisiontree()
1.1.6.000:
- fixed __version__
- fixed __all__ order
- added decisiontree()
1.1.5.003:
- added pca
1.1.5.002:
- reduced import list
- added kmeans clustering engine
1.1.5.001:
- simplified regression by using .to(device)
1.1.5.000:
- added polynomial regression to regression(); untested
1.1.4.000:
- added trueskill()
1.1.3.002:
- renamed regression class to Regression, regression_engine() to regression gliko2_engine class to Gliko2
1.1.3.001:
- changed glicko2() to return tuple instead of array
1.1.3.000:
- added glicko2_engine class and glicko()
- verified glicko2() accuracy
1.1.2.003:
- fixed elo()
1.1.2.002:
- added elo()
- elo() has bugs to be fixed
1.1.2.001:
- readded regrression import
1.1.2.000:
- integrated regression.py as regression class
- removed regression import
- fixed metadata for regression class
- fixed metadata for analysis class
1.1.1.001:
- regression_engine() bug fixes, now actaully regresses
1.1.1.000:
- added regression_engine()
- added all regressions except polynomial
1.1.0.007:
- updated _init_device()
1.1.0.006:
- removed useless try statements
1.1.0.005:
- removed impossible outcomes
1.1.0.004:
- added performance metrics (r^2, mse, rms)
1.1.0.003:
- resolved nopython mode for mean, median, stdev, variance
1.1.0.002:
- snapped (removed) majority of uneeded imports
- forced object mode (bad) on all jit
- TODO: stop numba complaining about not being able to compile in nopython mode
1.1.0.001:
- removed from sklearn import * to resolve uneeded wildcard imports
1.1.0.000:
- removed c_entities,nc_entities,obstacles,objectives from __all__
- applied numba.jit to all functions
- depreciated and removed stdev_z_split
- cleaned up histo_analysis to include numpy and numba.jit optimizations
- depreciated and removed all regression functions in favor of future pytorch optimizer
- depreciated and removed all nonessential functions (basic_analysis, benchmark, strip_data)
- optimized z_normalize using sklearn.preprocessing.normalize
- TODO: implement kernel/function based pytorch regression optimizer
1.0.9.000:
- refactored
- numpyed everything
- removed stats in favor of numpy functions
1.0.8.005:
- minor fixes
1.0.8.004:
- removed a few unused dependencies
1.0.8.003:
- added p_value function
1.0.8.002:
- updated __all__ correctly to contain changes made in v 1.0.8.000 and v 1.0.8.001
1.0.8.001:
- refactors
- bugfixes
1.0.8.000:
- depreciated histo_analysis_old
- depreciated debug
- altered basic_analysis to take array data instead of filepath
- refactor
- optimization
1.0.7.002:
- bug fixes
1.0.7.001:
- bug fixes
1.0.7.000:
- added tanh_regression (logistical regression)
- bug fixes
1.0.6.005:
- added z_normalize function to normalize dataset
- bug fixes
1.0.6.004:
- bug fixes
1.0.6.003:
- bug fixes
1.0.6.002:
- bug fixes
1.0.6.001:
- corrected __all__ to contain all of the functions
1.0.6.000:
- added calc_overfit, which calculates two measures of overfit, error and performance
- added calculating overfit to optimize_regression
1.0.5.000:
- added optimize_regression function, which is a sample function to find the optimal regressions
- optimize_regression function filters out some overfit funtions (functions with r^2 = 1)
- planned addition: overfit detection in the optimize_regression function
1.0.4.002:
- added __changelog__
- updated debug function with log and exponential regressions
1.0.4.001:
- added log regressions
- added exponential regressions
- added log_regression and exp_regression to __all__
1.0.3.008:
- added debug function to further consolidate functions
1.0.3.007:
- added builtin benchmark function
- added builtin random (linear) data generation function
- added device initialization (_init_device)
1.0.3.006:
- reorganized the imports list to be in alphabetical order
- added search and regurgitate functions to c_entities, nc_entities, obstacles, objectives
1.0.3.005:
- major bug fixes
- updated historical analysis
- depreciated old historical analysis
1.0.3.004:
- added __version__, __author__, __all__
- added polynomial regression
- added root mean squared function
- added r squared function
1.0.3.003:
- bug fixes
- added c_entities
1.0.3.002:
- bug fixes
- added nc_entities, obstacles, objectives
- consolidated statistics.py to analysis.py
1.0.3.001:
- compiled 1d, column, and row basic stats into basic stats function
1.0.3.000:
- added historical analysis function
1.0.2.xxx:
- added z score test
1.0.1.xxx:
- major bug fixes
1.0.0.xxx:
- added loading csv
- added 1d, column, row basic stats
"""
__author__ = (
"Arthur Lu <learthurgo@gmail.com>",
"Jacob Levine <jlevine@imsa.edu>",
)
__all__ = [
'load_csv',
'basic_stats',
'z_score',
'z_normalize',
'histo_analysis',
'regression',
'elo',
'glicko2',
'trueskill',
'RegressionMetrics',
'ClassificationMetrics',
'kmeans',
'pca',
'decisiontree',
'knn_classifier',
'knn_regressor',
'NaiveBayes',
'SVM',
'random_forest_classifier',
'random_forest_regressor',
# all statistics functions left out due to integration in other functions
]
# now back to your regularly scheduled programming:
# imports (now in alphabetical order! v 1.0.3.006):
import csv
from analysis import glicko2 as Glicko2
import numba
from numba import jit
import numpy as np
import scipy
from scipy import *
import sklearn
from sklearn import *
from analysis import trueskill as Trueskill
class error(ValueError):
pass
def load_csv(filepath):
with open(filepath, newline='') as csvfile:
file_array = np.array(list(csv.reader(csvfile)))
csvfile.close()
return file_array
# expects 1d array
@jit(forceobj=True)
def basic_stats(data):
data_t = np.array(data).astype(float)
_mean = mean(data_t)
_median = median(data_t)
_stdev = stdev(data_t)
_variance = variance(data_t)
_min = npmin(data_t)
_max = npmax(data_t)
return _mean, _median, _stdev, _variance, _min, _max
# returns z score with inputs of point, mean and standard deviation of spread
@jit(forceobj=True)
def z_score(point, mean, stdev):
score = (point - mean) / stdev
return score
# expects 2d array, normalizes across all axes
@jit(forceobj=True)
def z_normalize(array, *args):
array = np.array(array)
for arg in args:
array = sklearn.preprocessing.normalize(array, axis = arg)
return array
@jit(forceobj=True)
# expects 2d array of [x,y]
def histo_analysis(hist_data):
if(len(hist_data[0]) > 2):
hist_data = np.array(hist_data)
derivative = np.array(len(hist_data) - 1, dtype = float)
t = np.diff(hist_data)
derivative = t[1] / t[0]
np.sort(derivative)
return basic_stats(derivative)[0], basic_stats(derivative)[3]
else:
return None
def regression(inputs, outputs, args): # inputs, outputs expects N-D array
X = np.array(inputs)
y = np.array(outputs)
regressions = []
if 'lin' in args: # formula: ax + b
try:
def func(x, a, b):
return a * x + b
popt, pcov = scipy.optimize.curve_fit(func, X, y)
regressions.append((popt.flatten().tolist(), None))
except Exception as e:
pass
if 'log' in args: # formula: a log (b(x + c)) + d
try:
def func(x, a, b, c, d):
return a * np.log(b*(x + c)) + d
popt, pcov = scipy.optimize.curve_fit(func, X, y)
regressions.append((popt.flatten().tolist(), None))
except Exception as e:
pass
if 'exp' in args: # formula: a e ^ (b(x + c)) + d
try:
def func(x, a, b, c, d):
return a * np.exp(b*(x + c)) + d
popt, pcov = scipy.optimize.curve_fit(func, X, y)
regressions.append((popt.flatten().tolist(), None))
except Exception as e:
pass
if 'ply' in args: # formula: a + bx^1 + cx^2 + dx^3 + ...
inputs = np.array([inputs])
outputs = np.array([outputs])
plys = []
limit = len(outputs[0])
for i in range(2, limit):
model = sklearn.preprocessing.PolynomialFeatures(degree = i)
model = sklearn.pipeline.make_pipeline(model, sklearn.linear_model.LinearRegression())
model = model.fit(np.rot90(inputs), np.rot90(outputs))
params = model.steps[1][1].intercept_.tolist()
params = np.append(params, model.steps[1][1].coef_[0].tolist()[1::])
params.flatten()
params = params.tolist()
plys.append(params)
regressions.append(plys)
if 'sig' in args: # formula: a tanh (b(x + c)) + d
try:
def func(x, a, b, c, d):
return a * np.tanh(b*(x + c)) + d
popt, pcov = scipy.optimize.curve_fit(func, X, y)
regressions.append((popt.flatten().tolist(), None))
except Exception as e:
pass
return regressions
class Metrics:
def elo(starting_score, opposing_score, observed, N, K):
expected = 1/(1+10**((np.array(opposing_score) - starting_score)/N))
return starting_score + K*(np.sum(observed) - np.sum(expected))
def glicko2(starting_score, starting_rd, starting_vol, opposing_score, opposing_rd, observations):
player = Glicko2.Glicko2(rating = starting_score, rd = starting_rd, vol = starting_vol)
player.update_player([x for x in opposing_score], [x for x in opposing_rd], observations)
return (player.rating, player.rd, player.vol)
def trueskill(teams_data, observations): # teams_data is array of array of tuples ie. [[(mu, sigma), (mu, sigma), (mu, sigma)], [(mu, sigma), (mu, sigma), (mu, sigma)]]
team_ratings = []
for team in teams_data:
team_temp = ()
for player in team:
player = Trueskill.Rating(player[0], player[1])
team_temp = team_temp + (player,)
team_ratings.append(team_temp)
return Trueskill.rate(team_ratings, ranks=observations)
class RegressionMetrics():
def __new__(cls, predictions, targets):
return cls.r_squared(cls, predictions, targets), cls.mse(cls, predictions, targets), cls.rms(cls, predictions, targets)
def r_squared(self, predictions, targets): # assumes equal size inputs
return sklearn.metrics.r2_score(targets, predictions)
def mse(self, predictions, targets):
return sklearn.metrics.mean_squared_error(targets, predictions)
def rms(self, predictions, targets):
return math.sqrt(sklearn.metrics.mean_squared_error(targets, predictions))
class ClassificationMetrics():
def __new__(cls, predictions, targets):
return cls.cm(cls, predictions, targets), cls.cr(cls, predictions, targets)
def cm(self, predictions, targets):
return sklearn.metrics.confusion_matrix(targets, predictions)
def cr(self, predictions, targets):
return sklearn.metrics.classification_report(targets, predictions)
@jit(nopython=True)
def mean(data):
return np.mean(data)
@jit(nopython=True)
def median(data):
return np.median(data)
@jit(nopython=True)
def stdev(data):
return np.std(data)
@jit(nopython=True)
def variance(data):
return np.var(data)
@jit(nopython=True)
def npmin(data):
return np.amin(data)
@jit(nopython=True)
def npmax(data):
return np.amax(data)
@jit(forceobj=True)
def kmeans(data, n_clusters=8, init="k-means++", n_init=10, max_iter=300, tol=0.0001, precompute_distances="auto", verbose=0, random_state=None, copy_x=True, n_jobs=None, algorithm="auto"):
kernel = sklearn.cluster.KMeans(n_clusters = n_clusters, init = init, n_init = n_init, max_iter = max_iter, tol = tol, precompute_distances = precompute_distances, verbose = verbose, random_state = random_state, copy_x = copy_x, n_jobs = n_jobs, algorithm = algorithm)
kernel.fit(data)
predictions = kernel.predict(data)
centers = kernel.cluster_centers_
return centers, predictions
@jit(forceobj=True)
def pca(data, n_components = None, copy = True, whiten = False, svd_solver = "auto", tol = 0.0, iterated_power = "auto", random_state = None):
kernel = sklearn.decomposition.PCA(n_components = n_components, copy = copy, whiten = whiten, svd_solver = svd_solver, tol = tol, iterated_power = iterated_power, random_state = random_state)
return kernel.fit_transform(data)
@jit(forceobj=True)
def decisiontree(data, labels, test_size = 0.3, criterion = "gini", splitter = "default", max_depth = None): #expects *2d data and 1d labels
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.tree.DecisionTreeClassifier(criterion = criterion, splitter = splitter, max_depth = max_depth)
model = model.fit(data_train,labels_train)
predictions = model.predict(data_test)
metrics = ClassificationMetrics(predictions, labels_test)
return model, metrics
class KNN:
def knn_classifier(data, labels, test_size = 0.3, algorithm='auto', leaf_size=30, metric='minkowski', metric_params=None, n_jobs=None, n_neighbors=5, p=2, weights='uniform'): #expects *2d data and 1d labels post-scaling
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.neighbors.KNeighborsClassifier()
model.fit(data_train, labels_train)
predictions = model.predict(data_test)
return model, ClassificationMetrics(predictions, labels_test)
def knn_regressor(data, outputs, test_size, n_neighbors = 5, weights = "uniform", algorithm = "auto", leaf_size = 30, p = 2, metric = "minkowski", metric_params = None, n_jobs = None):
data_train, data_test, outputs_train, outputs_test = sklearn.model_selection.train_test_split(data, outputs, test_size=test_size, random_state=1)
model = sklearn.neighbors.KNeighborsRegressor(n_neighbors = n_neighbors, weights = weights, algorithm = algorithm, leaf_size = leaf_size, p = p, metric = metric, metric_params = metric_params, n_jobs = n_jobs)
model.fit(data_train, outputs_train)
predictions = model.predict(data_test)
return model, RegressionMetrics(predictions, outputs_test)
class NaiveBayes:
def guassian(self, data, labels, test_size = 0.3, priors = None, var_smoothing = 1e-09):
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.naive_bayes.GaussianNB(priors = priors, var_smoothing = var_smoothing)
model.fit(data_train, labels_train)
predictions = model.predict(data_test)
return model, ClassificationMetrics(predictions, labels_test)
def multinomial(self, data, labels, test_size = 0.3, alpha=1.0, fit_prior=True, class_prior=None):
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.naive_bayes.MultinomialNB(alpha = alpha, fit_prior = fit_prior, class_prior = class_prior)
model.fit(data_train, labels_train)
predictions = model.predict(data_test)
return model, ClassificationMetrics(predictions, labels_test)
def bernoulli(self, data, labels, test_size = 0.3, alpha=1.0, binarize=0.0, fit_prior=True, class_prior=None):
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.naive_bayes.BernoulliNB(alpha = alpha, binarize = binarize, fit_prior = fit_prior, class_prior = class_prior)
model.fit(data_train, labels_train)
predictions = model.predict(data_test)
return model, ClassificationMetrics(predictions, labels_test)
def complement(self, data, labels, test_size = 0.3, alpha=1.0, fit_prior=True, class_prior=None, norm=False):
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
model = sklearn.naive_bayes.ComplementNB(alpha = alpha, fit_prior = fit_prior, class_prior = class_prior, norm = norm)
model.fit(data_train, labels_train)
predictions = model.predict(data_test)
return model, ClassificationMetrics(predictions, labels_test)
class SVM:
class CustomKernel:
def __new__(cls, C, kernel, degre, gamma, coef0, shrinking, probability, tol, cache_size, class_weight, verbose, max_iter, decision_function_shape, random_state):
return sklearn.svm.SVC(C = C, kernel = kernel, gamma = gamma, coef0 = coef0, shrinking = shrinking, probability = probability, tol = tol, cache_size = cache_size, class_weight = class_weight, verbose = verbose, max_iter = max_iter, decision_function_shape = decision_function_shape, random_state = random_state)
class StandardKernel:
def __new__(cls, kernel, C=1.0, degree=3, gamma='auto_deprecated', coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, class_weight=None, verbose=False, max_iter=-1, decision_function_shape='ovr', random_state=None):
return sklearn.svm.SVC(C = C, kernel = kernel, gamma = gamma, coef0 = coef0, shrinking = shrinking, probability = probability, tol = tol, cache_size = cache_size, class_weight = class_weight, verbose = verbose, max_iter = max_iter, decision_function_shape = decision_function_shape, random_state = random_state)
class PrebuiltKernel:
class Linear:
def __new__(cls):
return sklearn.svm.SVC(kernel = 'linear')
class Polynomial:
def __new__(cls, power, r_bias):
return sklearn.svm.SVC(kernel = 'polynomial', degree = power, coef0 = r_bias)
class RBF:
def __new__(cls, gamma):
return sklearn.svm.SVC(kernel = 'rbf', gamma = gamma)
class Sigmoid:
def __new__(cls, r_bias):
return sklearn.svm.SVC(kernel = 'sigmoid', coef0 = r_bias)
def fit(self, kernel, train_data, train_outputs): # expects *2d data, 1d labels or outputs
return kernel.fit(train_data, train_outputs)
def eval_classification(self, kernel, test_data, test_outputs):
predictions = kernel.predict(test_data)
return ClassificationMetrics(predictions, test_outputs)
def eval_regression(self, kernel, test_data, test_outputs):
predictions = kernel.predict(test_data)
return RegressionMetrics(predictions, test_outputs)
def random_forest_classifier(data, labels, test_size, n_estimators="warn", criterion="gini", max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features="auto", max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False, class_weight=None):
data_train, data_test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, test_size=test_size, random_state=1)
kernel = sklearn.ensemble.RandomForestClassifier(n_estimators = n_estimators, criterion = criterion, max_depth = max_depth, min_samples_split = min_samples_split, min_samples_leaf = min_samples_leaf, min_weight_fraction_leaf = min_weight_fraction_leaf, max_leaf_nodes = max_leaf_nodes, min_impurity_decrease = min_impurity_decrease, bootstrap = bootstrap, oob_score = oob_score, n_jobs = n_jobs, random_state = random_state, verbose = verbose, warm_start = warm_start, class_weight = class_weight)
kernel.fit(data_train, labels_train)
predictions = kernel.predict(data_test)
return kernel, ClassificationMetrics(predictions, labels_test)
def random_forest_regressor(data, outputs, test_size, n_estimators="warn", criterion="mse", max_depth=None, min_samples_split=2, min_samples_leaf=1, min_weight_fraction_leaf=0.0, max_features="auto", max_leaf_nodes=None, min_impurity_decrease=0.0, min_impurity_split=None, bootstrap=True, oob_score=False, n_jobs=None, random_state=None, verbose=0, warm_start=False):
data_train, data_test, outputs_train, outputs_test = sklearn.model_selection.train_test_split(data, outputs, test_size=test_size, random_state=1)
kernel = sklearn.ensemble.RandomForestRegressor(n_estimators = n_estimators, criterion = criterion, max_depth = max_depth, min_samples_split = min_samples_split, min_weight_fraction_leaf = min_weight_fraction_leaf, max_features = max_features, max_leaf_nodes = max_leaf_nodes, min_impurity_decrease = min_impurity_decrease, min_impurity_split = min_impurity_split, bootstrap = bootstrap, oob_score = oob_score, n_jobs = n_jobs, random_state = random_state, verbose = verbose, warm_start = warm_start)
kernel.fit(data_train, outputs_train)
predictions = kernel.predict(data_test)
return kernel, RegressionMetrics(predictions, outputs_test)