We consider a Bayesian forecast aggregation model where n experts, after observing private signals about an unknown binary event, report th eir posterior beliefs about the event to a principal, who then aggregates the repor ts into a single prediction for the event. The signals of the experts and the outcome of the event follow a joint distribution that is unknown to the principal, but th e principal has access to i.i.d. "samples" from the distribution, where each sampl e is a tuple of the experts' reports (not signals) and the realization of the even t. Using these samples, the principal aims to find an ε -approximately optimal aggregator, where optimal-ity is measured in terms of the expected squared distance bet ween the aggregated prediction and the realization of the event.

Furthermore, we theoretically and empirically show that softmax can be viewed as a special case of logistic-softmax and logistic-softmax induces a larger family of data distribution than softmax.

In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data.

A popular perspective in Reinforcement learning (RL) casts the problem as probabilistic inference on a graphical model of the Markov decision process (MDP). The core object of study is the probability of each state-action pair being visited under the optimal policy.

Theoretically, we show that it is possible for our approach to simultaneously improve both accuracy and fairness--in contrast to standard fairness approaches that suffer from tradeoffs. Empirically, we show that our technique improves accuracy on weak supervision baselines by as much as 32% while reducing demographic parity gap by 82.5%.

Machine learning tools often rely on embedding text as vectors of real numbers. In this paper, we study how the semantic structure of language is encoded in the algebraic structure of such embeddings.

We show that our "Joint Structure and