Learn the data programming parameters alpha and beta. Args: - with_label: Do we use y or not? If using label, use the train set and

Load in dataset from task_name depending on where files are saved. - num_elts = number of ``choices'' to use in the multiple-choice setup.

Computes the probability Pr(y = 1 | votes).

If a graph is triangulated (e.g. if a junction tree factorization exists).

Learn the neighborhood graph for a vertex. Args: - m: number of prompts - vertex: the index of the prompt we are selecting as the re

Structure learning algorithm (Ising model selection) from Ravikumar (2010). Args: - votes: n_train x m array of training votes - gol

Initialize the PGM by computing its junction tree factorization (c_tree and c_data) and by computing individual LF accuracy a

Computes H(Y | votes) ~= -1/n sum_i sum_y' Pr(y = y' | votes_j) log Pr(y = y' | votes_j). Uses learned distribution as true

Computes H(Y | MV output) = -1/n sum_i sum_k Pr(y = y_k | y-hat_i) log Pr(y = y_k | y-hat_i)

Computes H(Y | WS output) = -1/n sum_i sum_j Pr(y-hat = y_j | lfs(x_i)) * sum_k Pr(y = y_k | y-hat = y_j) log Pr(y = y_k | y-hat = y_j)

For multi-class, data programming reduces into one-vs-all subproblems and picking the highest Pr(y | votes) from each of those.

Weighting rule 1: Pr(y | votes) ~ sum_i 1{vote_i = y} * exp(-eta*loss_i) Weighting rule 2: Pr(y | votes) ~ exp(sum_i eta * accuracy *

For multi-class, FlyingSquid reduces into one-vs-all subproblems and picking the highest Pr(y | votes) from each of those.

Logistic regression baseline. Args: - pairwise: if true, we scale everything to [-1, 1] and look at vote_i * vote_j as (m c

Use Snorkel AI's label model. Under the hood: Metal "forward" algorithm.