pma.py

import numpy as np
import tensorflow as tf
from tensorflow.keras import layers, Model
from scipy.stats import multivariate_normal
from scipy.integrate import quad
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, mean_absolute_error
import statsmodels.api as sm

class DilatedCausalConv1D(layers.Layer):
    def __init__(self, filters, kernel_size, dilation_rate):
        super(DilatedCausalConv1D, self).__init__()
        self.conv = layers.Conv1D(filters=filters,
                                  kernel_size=kernel_size,
                                  padding='causal',
                                  dilation_rate=dilation_rate)
    
    def call(self, inputs):
        return self.conv(inputs)

class MTCNLayer(layers.Layer):
    def __init__(self, filters, kernel_size, dilation_rate, dropout_rate):
        super(MTCNLayer, self).__init__()
        self.conv = DilatedCausalConv1D(filters, kernel_size, dilation_rate)
        self.norm = layers.LayerNormalization()
        self.dropout = layers.Dropout(dropout_rate)
        self.activation = layers.Activation('relu')
    
    def call(self, inputs):
        x = self.conv(inputs)
        x = self.norm(x)
        x = self.activation(x)
        return self.dropout(x)

class MTCN(Model):
    def __init__(self, num_layers, kernel_size, filters, dropout_rate, output_dim):
        super(MTCN, self).__init__()
        self.layers_list = [MTCNLayer(filters, kernel_size, 2**i, dropout_rate) 
                            for i in range(num_layers)]
        self.final_conv = layers.Conv1D(filters=output_dim, kernel_size=1)
    
    def call(self, inputs):
        x = inputs
        for layer in self.layers_list:
            x = layer(x)
        return self.final_conv(x)

class PredictiveModelingAlgorithm:
    def __init__(self, input_dim, output_dim, num_layers=8, kernel_size=3, num_filters=64, dropout_rate=0.2, num_ensemble=5):
        self.input_dim = input_dim
        self.output_dim = output_dim
        self.num_ensemble = num_ensemble
        self.models = [MTCN(num_layers, kernel_size, num_filters, dropout_rate, output_dim) 
                       for _ in range(num_ensemble)]
        self.compile_models()

    def compile_models(self):
        for model in self.models:
            model.compile(optimizer='adam', loss='mse', metrics=['mae'])

    def train(self, X, y, epochs=100, batch_size=32, validation_split=0.2):
        X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=validation_split)
        histories = []
        for model in self.models:
            history = model.fit(X_train, y_train, epochs=epochs, batch_size=batch_size, 
                                validation_data=(X_val, y_val), verbose=0)
            histories.append(history)
        return histories

    def predict(self, X):
        predictions = [model.predict(X) for model in self.models]
        return np.mean(predictions, axis=0), np.std(predictions, axis=0)

    def generate_scenarios(self, initial_state, num_scenarios, time_steps):
        scenarios = []
        for _ in range(num_scenarios):
            scenario = [initial_state]
            for _ in range(time_steps - 1):
                next_state_mean, next_state_std = self.predict(np.array([scenario[-1]]))
                next_state = np.random.normal(next_state_mean[0, -1, :], next_state_std[0, -1, :])
                scenario.append(next_state)
            scenarios.append(np.array(scenario))
        return np.array(scenarios)

    def calculate_posterior(self, prior, likelihood, data):
        prior_mean, prior_cov = prior
        likelihood_mean, likelihood_cov = likelihood
        posterior_cov = np.linalg.inv(np.linalg.inv(prior_cov) + np.linalg.inv(likelihood_cov))
        posterior_mean = posterior_cov @ (np.linalg.inv(prior_cov) @ prior_mean + np.linalg.inv(likelihood_cov) @ data)
        return posterior_mean, posterior_cov

    def integrate_posterior(self, posterior, func):
        posterior_mean, posterior_cov = posterior
        def integrand(x):
            return func(x) * multivariate_normal.pdf(x, mean=posterior_mean, cov=posterior_cov)
        
        # Monte Carlo integration
        num_samples = 10000
        samples = multivariate_normal.rvs(mean=posterior_mean, cov=posterior_cov, size=num_samples)
        return np.mean([func(s) for s in samples])

    def handle_black_swan(self, X, threshold=3):
        # Detect and handle potential black swan events using extreme value theory
        extreme_events = []
        for i in range(X.shape[1]):
            series = X[:, i]
            z_scores = (series - np.mean(series)) / np.std(series)
            extreme_events.append(np.where(np.abs(z_scores) > threshold)[0])
        
        # Adjust predictions for extreme events
        adjusted_X = X.copy()
        for i, events in enumerate(extreme_events):
            if len(events) > 0:
                adjusted_X[:, i] = sm.robust.robust_linear_model.RLM(
                    sm.add_constant(np.arange(len(X))), X[:, i]
                ).fit().predict(sm.add_constant(np.arange(len(X))))
        
        return adjusted_X, extreme_events

    def evaluate(self, X_test, y_test):
        y_pred_mean, y_pred_std = self.predict(X_test)
        mse = mean_squared_error(y_test, y_pred_mean)
        mae = mean_absolute_error(y_test, y_pred_mean)
        
        # Calculate CRPS (Continuous Ranked Probability Score)
        def crps_gaussian(y_true, mu, sig):
            z = (y_true - mu) / sig
            return sig * (z * (2 * norm.cdf(z) - 1) + 2 * norm.pdf(z) - 1 / np.sqrt(np.pi))
        
        crps = np.mean([crps_gaussian(y_test[i], y_pred_mean[i], y_pred_std[i]) 
                        for i in range(len(y_test))])
        
        return {
            'MSE': mse,
            'MAE': mae,
            'CRPS': crps
        }

    def forecast_with_uncertainty(self, X, num_samples=1000):
        predictions = []
        for _ in range(num_samples):
            model = np.random.choice(self.models)
            predictions.append(model.predict(X))
        
        mean_prediction = np.mean(predictions, axis=0)
        lower_bound = np.percentile(predictions, 2.5, axis=0)
        upper_bound = np.percentile(predictions, 97.5, axis=0)
        
        return mean_prediction, lower_bound, upper_bound

    def analyze_feature_importance(self, X, y):
        feature_importance = []
        for model in self.models:
            # Use integrated gradients for feature importance
            ig = IntegratedGradients(model)
            attributions = ig.attribute(X, target=y, n_steps=50)
            feature_importance.append(np.mean(np.abs(attributions), axis=0))
        
        return np.mean(feature_importance, axis=0)

# Additional utility functions

def IntegratedGradients(model):
    # Placeholder for the IntegratedGradients method
    # In a real implementation, this would be imported from a library like captum
    class IG:
        def __init__(self, model):
            self.model = model
        
        def attribute(self, inputs, target, n_steps):
            # Placeholder implementation
            return np.random.rand(*inputs.shape)
    
    return IG(model)