Foundry $> Alpha Obsessed
Quants
import pandas as pd import numpy as np def forward(V, a, b, initial_distribution): alpha = np.zeros((V.shape[0], a.shape[0])) alpha[0, :] = initial_distribution * b[:, V[0]] for t in range(1, V.shape[0]): for j in range(a.shape[0]): # Matrix Computation Steps # ((1x2) . (1x2)) * (1) # (1) * (1) alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]] return alpha def backward(V, a, b): beta = np.zeros((V.shape[0], a.shape[0])) # setting beta(T) = 1 beta[V.shape[0] - 1] = np.ones((a.shape[0])) # Loop in backward way from T-1 to # Due to python indexing the actual loop will be T-2 to 0 for t in range(V.shape[0] - 2, -1, -1): for j in range(a.shape[0]): beta[t, j] = (beta[t + 1] * b[:, V[t + 1]]).dot(a[j, :]) return beta def baum_welch(V, a, b, initial_distribution, n_iter=100): M = a.shape[0] T = len(V) for n in range(n_iter): alpha = forward(V, a, b, initial_distribution) beta = backward(V, a, b) xi = np.zeros((M, M, T - 1)) for t in range(T - 1): denominator = np.dot(np.dot(alpha[t, :].T, a) * b[:, V[t + 1]].T, beta[t + 1, :]) for i in range(M): numerator = alpha[t, i] * a[i, :] * b[:, V[t + 1]].T * beta[t + 1, :].T xi[i, :, t] = numerator / denominator gamma = np.sum(xi, axis=1) a = np.sum(xi, 2) / np.sum(gamma, axis=1).reshape((-1, 1)) # Add additional T'th element in gamma gamma = np.hstack((gamma, np.sum(xi[:, :, T - 2], axis=0).reshape((-1, 1)))) K = b.shape[1] denominator = np.sum(gamma, axis=1) for l in range(K): b[:, l] = np.sum(gamma[:, V == l], axis=1) b = np.divide(b, denominator.reshape((-1, 1))) return {"a":a, "b":b} data = pd.read_csv('data_python.csv') V = data['Visible'].values # Transition Probabilities a = np.ones((2, 2)) a = a / np.sum(a, axis=1) # Emission Probabilities b = np.array(((1, 3, 5), (2, 4, 6))) b = b / np.sum(b, axis=1).reshape((-1, 1)) # Equal Probabilities for the initial distribution initial_distribution = np.array((0.5, 0.5)) print(baum_welch(V, a, b, initial_distribution, n_iter=100))
import pandas as pd import numpy as np def forward(V, a, b, initial_distribution): alpha = np.zeros((V.shape[0], a.shape[0])) alpha[0, :] = initial_distribution * b[:, V[0]] for t in range(1, V.shape[0]): for j in range(a.shape[0]): # Matrix Computation Steps # ((1x2) . (1x2)) * (1) # (1) * (1) alpha[t, j] = alpha[t - 1].dot(a[:, j]) * b[j, V[t]] return alpha def backward(V, a, b): beta = np.zeros((V.shape[0], a.shape[0])) # setting beta(T) = 1 beta[V.shape[0] - 1] = np.ones((a.shape[0])) # Loop in backward way from T-1 to # Due to python indexing the actual loop will be T-2 to 0 for t in range(V.shape[0] - 2, -1, -1): for j in range(a.shape[0]): beta[t, j] = (beta[t + 1] * b[:, V[t + 1]]).dot(a[j, :]) return beta def baum_welch(V, a, b, initial_distribution, n_iter=100): M = a.shape[0] T = len(V) for n in range(n_iter): alpha = forward(V, a, b, initial_distribution) beta = backward(V, a, b) xi = np.zeros((M, M, T - 1)) for t in range(T - 1): denominator = np.dot(np.dot(alpha[t, :].T, a) * b[:, V[t + 1]].T, beta[t + 1, :]) for i in range(M): numerator = alpha[t, i] * a[i, :] * b[:, V[t + 1]].T * beta[t + 1, :].T xi[i, :, t] = numerator / denominator gamma = np.sum(xi, axis=1) a = np.sum(xi, 2) / np.sum(gamma, axis=1).reshape((-1, 1)) # Add additional T'th element in gamma gamma = np.hstack((gamma, np.sum(xi[:, :, T - 2], axis=0).reshape((-1, 1)))) K = b.shape[1] denominator = np.sum(gamma, axis=1) for l in range(K): b[:, l] = np.sum(gamma[:, V == l], axis=1) b = np.divide(b, denominator.reshape((-1, 1))) return {"a":a, "b":b} data = pd.read_csv('data_python.csv') V = data['Visible'].values # Transition Probabilities a = np.ones((2, 2)) a = a / np.sum(a, axis=1) # Emission Probabilities b = np.array(((1, 3, 5), (2, 4, 6))) b = b / np.sum(b, axis=1).reshape((-1, 1)) # Equal Probabilities for the initial distribution initial_distribution = np.array((0.5, 0.5)) print(baum_welch(V, a, b, initial_distribution, n_iter=100))
mission
Services
Professional services focused on emerging technologies such as Generative AI, Quantum computing and Web 3.0.
STACK
Proprietary data pipelines, algorithms & tools for time series data analysis. Advancing research through novel uses of generative AI models.
Research
The Foundry is a collective of alpha-obsessed Quants with diverse backgrounds, researching novel machine learning methods for time series data.
vision
We are dedicated researchers and consultants testing the limits of the box; applying new modalities to old systems. Focused on AI-driven strategies, and as a self-organizing collective of the brightest minds, the Foundry’s goal is a break-through the conventional barriers that [re]defines the way financial systems are modeled today.
