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The Landscape of Volleyball 1. Division West Women
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The Importance of Statistics
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The Role of Technology in Volleyball
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<|repo_name|>DanielAldrich/bayesian-portfolio<|file_sep|>/bayesian_portfolio.py
import numpy as np
from scipy.stats import norm
from scipy.optimize import minimize
import pandas as pd
class BayesianPortfolio(object):
def __init__(self,
prior_mean=None,
prior_cov=None,
risk_aversion=1,
gamma=0,
target_return=None,
verbose=False):
self.verbose = verbose
self.risk_aversion = risk_aversion
self.gamma = gamma
if target_return is not None:
self.target_return = target_return
else:
self.target_return = None
if prior_mean is not None:
self.prior_mean = prior_mean
else:
self.prior_mean = None
if prior_cov is not None:
self.prior_cov = prior_cov
else:
self.prior_cov = None
if self.prior_mean is None or self.prior_cov is None:
raise ValueError('Please provide prior mean vector (mu)
or covariance matrix (Sigma)')
if self.target_return is not None:
if len(self.target_return) != len(self.prior_mean):
raise ValueError('target return vector has wrong length')
def fit(self,X,y):
if not isinstance(X,pd.DataFrame):
raise TypeError('X must be a pandas DataFrame')
if y.shape[0] != X.shape[0]:
raise ValueError('y must have same number of rows as X')
n = X.shape[0]
p = X.shape[1]
# compute sample mean vector
xbar = np.mean(X,axis=0)
# compute sample covariance matrix
S = np.cov(X.T)
# compute posterior mean vector
Sigma_inv = np.linalg.inv(self.prior_cov)
mu_inv_Sigma_mu = np.dot(np.dot(Sigma_inv,self.prior_mean),self.prior_mean.T)
posterior_mu_numerator = np.dot(Sigma_inv,self.prior_mean) + n*np.dot(xbar,y)
posterior_mu_denominator = Sigma_inv + n*S + mu_inv_Sigma_mu*np.eye(p)
posterior_mu = np.dot(posterior_mu_numerator,np.linalg.inv(posterior_mu_denominator))
# compute posterior covariance matrix
posterior_Sigma_numerator = Sigma_inv + n*np.eye(p)
posterior_Sigma_denominator = Sigma_inv + n*S + mu_inv_Sigma_mu*np.eye(p)
posterior_Sigma = np.dot(np.linalg.inv(posterior_Sigma_numerator),
posterior_Sigma_denominator)
# print('posterior mean:n',posterior_mu)
# print('posterior covariance:n',posterior_Sigma)
# print('n')
# print('sample mean:n',xbar)
# print('sample covariance:n',S)
# print('n')
# print('prior mean:n',self.prior_mean)
# print('prior covariance:n',self.prior_cov)
# fig1=plt.figure()
# plt.scatter(X.iloc[:,0],X.iloc[:,1],c=y,cmap='viridis')
# plt.show()
# fig1=plt.figure()
# ax=fig1.add_subplot(111)
# ax.plot(X.iloc[:,0],y,'.')
# plt.show()
# fig1=plt.figure()
# ax=fig1.add_subplot(111)
# ax.plot(y,'.')
# plt.show()
# fig1=plt.figure()
# ax=fig1.add_subplot(111)
# ax.plot(X.iloc[:,0],y,'.')
# # ax.set_xlim(-10,)
# # ax.set_ylim(-10,)
# # plt.ylim(-10,)
# # plt.xlim(-10,)
def _objective_function(self,x):
def simulate_data(n,p,rho,mu,sig,sig_e):
"""
Simulates data from multivariate normal distribution
Parameters
----------
n : int
number of samples
p : int
number of features
rho : float between -1 and +1 inclusive
correlation between features
mu : float
population mean
sig : float
population standard deviation
sig_e : float
standard deviation of noise
Returns
-------
X : pandas dataframe with shape (n,p)
simulated features
y : numpy array with shape (n,)
simulated response variable
***** Tag Data *****
ID: 3
description: The fit method performs Bayesian updating based on observed data.
start line: 46
end line: 106
dependencies:
- type: Method
name: __init__
start line: 13
end line: 45
context description: This method computes the posterior mean vector and covariance
matrix using Bayesian inference principles.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 4
advanced coding concepts: 4
interesting for students: 5
self contained: Y
*************
## Suggestions for complexity
1. **Dynamic Risk Aversion Adjustment**: Introduce logic that dynamically adjusts `risk_aversion` based on certain criteria derived from `X` or `y`, such as volatility measures.
2. **Hierarchical Bayesian Model**: Expand the current model into a hierarchical Bayesian framework where there are multiple levels of priors (e.g., hyper-priors).
3. **Monte Carlo Integration**: Implement Monte Carlo integration within `fit` method for approximating integrals required for computing the posterior distributions.
4. **Time Series Adaptation**: Modify the code to handle time series data by incorporating temporal dependencies using techniques like state-space models or Kalman filters.
5. **Custom Loss Function**: Allow users to specify custom loss functions that can be used within the `fit` method instead of standard likelihood-based methods.
## Conversation
<|user|>I need help with some advanced modification to my code snippet [SNIPPET]. Specifically, I want to introduce dynamic risk aversion adjustment based on some criteria derived from `X` or `y`. Can you guide me on how I might approach this?<|end|>
<|assistant|>Certainly! To introduce dynamic risk aversion adjustment based on criteria derived from `X` or `y`, we can add logic within your `fit` method that recalculates `self.risk_aversion` before computing the posterior mean vector and covariance matrix.
Here’s an example approach:
python
def fit(self,X,y):
if not isinstance(X,pd.DataFrame):
raise TypeError('X must be a pandas DataFrame')
if y.shape[0] != X.shape[0]:
raise ValueError('y must have same number of rows as X')
n = X.shape[0]
p = X.shape[1]
# Example criterion: Adjust risk aversion based on variance of y.
variance_y = np.var(y)
# Dynamic adjustment logic (example: higher variance increases risk aversion)
if variance_y > threshold_high:
self.risk_aversion *= high_risk_multiplier
elif variance_y < threshold_low:
self.risk_aversion *= low_risk_multiplier
# compute sample mean vector
xbar = np.mean(X,axis=0)
# compute sample covariance matrix
S = np.cov(X.T)
...
In this example:
- We define thresholds (`threshold_high`, `threshold_low`) and multipliers (`high_risk_multiplier`, `low_risk_multiplier`) that determine how risk aversion changes based on the variance of `y`.
- The risk aversion factor is dynamically adjusted before proceeding with computations.
Would you like me to refine this logic further or provide additional criteria?
[0]: import copy
[1]: import numpy as np
[2]: from sklearn.base import BaseEstimator
[3]: from darts.timeseries import TimeSeries
[4]: class Pipeline(BaseEstimator):
[5]: """Darts Pipeline.
[6]: A Pipeline sequentially applies a list of transforms (implementing fit/transform) followed by an estimator (implementing fit/predict).
[7]: Parameters
[8]: ----------
[9]: steps : list (PipelineStep tuple)
[10]: Examples
[11]: --------
[12]: >>> from darts import TimeSeriesRegressionBenchmark,sarimax_forecast_pipeline
[13]: >>> benchmark_results_dict=sarimax_forecast_pipeline.fit_and_evaluate(build_name="SARIMAX",target_length=12,n_jobs=-1,
[14]: >>> benchmark_cls=TimeSeriesRegressionBenchmark,n_evaluations=20,
[15]: >>> input_chunk_length=24,output_chunk_length=12)
[16]: """
[17]: def __init__(self, steps):
[18]: self.steps = steps
[19]: @property
[20]: def named_steps(self):
[21]: return dict((step_name_, step_) for step_name_, step_ in self.steps)
[22]: def _iter(self):
[23]: """Helper function."""
[24]: for step_name_, trans in self.steps:
[25]: yield step_name_, trans
[26]: def _pre_transform(self):
[27]: """Helper function."""
[28]: Xt = copy.deepcopy(self._tfrms)
[29]: for name, trf in reversed(list(self._iter())):
[30]: if hasattr(trf, "reverse_transform"):
[31]: Xt = trf.reverse_transform(Xt)
[32]: # infer feature types once only at beginning of chain reversal.
[33]: elif isinstance(trf, InferFeatureTypes):
[34]: pass
[35]: else:
[36]: raise ValueError("Step %r should implement reverse_transform" % name)
[37]: self._tfrms.pop()
[38]: # eliminate IdentityTransforms from chain.
[39]: if not isinstance(trf, (NoOpTransform)):
[40]: break
[41]: return Xt
[42]: def _transform_last(self):
[43]: """Helper function."""
[44]: Xt = copy.deepcopy(self._tfrms)
[45]: counter = -1
[46]: while True:
[47]: try:
trf = Xt[counter]
name,_=self.steps[counter]
if name=="standardize":
trf.mean_=trf.mean_.copy()
trf.std_=trf.std_.copy()
counter -= -1
Xt[counter].transform(last=True)
except IndexError:
break
counter -= -1
return Xt[-1]
***** Tag Data *****
ID: 3
description: The `_transform_last` method processes transformations in reverse order,
handling specific cases like 'standardize' by copying mean and std values before
applying transformations.
start line: 42
end line: 64
dependencies:
- type: Class
name: Pipeline
start line: 4
end line: 16
context description: This method focuses on transforming the last element after copying,
demonstrating advanced handling techniques including deep copies and special case-specific
operations.
algorithmic depth: 4
algorithmic depth external: N
obscurity: 5
advanced coding concepts: 4
interesting for students: DETAILED_REASONING_ABOUT_SPECIAL_CASE_HANDLING_EXAMPLES_IN_THE_SNIPPET_AND_THEIR_IMPACT_ON_TRANSFORMATIONS.
self contained: N
************
## Challenging Aspects
### Challenging Aspects in Above Code:
1. **Deep Copy Nuances**:
- The use of `deepcopy` suggests that transformations (`_tfrms`) involve mutable objects whose states must be preserved
