We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Our method involves a fast optimization based weighted clustering procedure augmented with geometric corrections, which overcomes the computational and statistical inefficiencies encountered by other techniques based on Gibbs sampling and variational inference, while achieving the accuracy comparable to that of a Gibbs sampler. The topic estimates produced by our method are shown to be statistically consistent under some conditions. The algorithm is evaluated with extensive experiments on simulated and real data.

Specifically, this non-iterative paradigm allows us to conduct inner-level optimization (value estimation) in training, while performing outer-level optimization (policy extraction) in testing. Naturally, such a paradigm raises three core questions that are not fully answered by prior non-iterative offline RL counterparts like rewardconditioned policy: Q1) What information should we transfer from the inner-level to the outer-level? Q2) What should we pay attention to when exploiting the transferred information for safe/confident outer-level optimization? Q3) What are the benefits of concurrently conducting outer-level optimization during testing? Motivated by model-based optimization (MBO), we propose DROP (Design fROm Policies), which fully answers the above questions. Specifically, in the inner-level, DROP decomposes offline data into multiple subsets and learns an MBO score model (A1). To keep safe exploitation to the score model in the outer-level, we explicitly learn a behavior embedding and introduce a conservative regularization (A2). During testing, we show that DROP permits test-time adaptation, enabling an adaptive inference across states (A3). Empirically, we find that DROP, compared to prior non-iterative offline RL counterparts, gains an average improvement probability of more than 80%, and achieves comparable or better performance compared to prior iterative baselines.

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events' emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlations in the past. In this paper, we propose a Bayesian nonparametric approach that considers both types of correlations via unifying and generalizing the hidden semi-Markov model and interaction point process model. The proposed approach can simultaneously model both the observations and arrival times of temporal events, and automatically determine the number of latent states from data.

Markov chain Monte Carlo (MCMC) is one of the main workhorses of probabilistic inference, but it is notoriously hard to measure the quality of approximate posterior samples. This challenge is particularly salient in black box inference methods, which can hide details and obscure inference failures. In this work, we extend the recently introduced bidirectional Monte Carlo technique to evaluate MCMC-based posterior inference algorithms. By running annealed importance sampling (AIS) chains both from prior to posterior and vice versa on simulated data, we upper bound in expectation the symmetrized KL divergence between the true posterior distribution and the distribution of approximate samples. We integrate our method into two probabilistic programming languages, WebPPL and Stan, and validate it on several models and datasets.

Leveraging the wealth of unlabeled data produced in recent years provides great potential for improving supervised models. When the cost of acquiring labels is high, probabilistic active learning methods can be used to greedily select the most informative data points to be labeled. However, for many large-scale problems standard greedy procedures become computationally infeasible and suffer from negligible model change. In this paper, we introduce a novel Bayesian batch active learning approach that mitigates these issues. Our approach is motivated by approximating the complete data posterior of the model parameters. While naive batch construction methods result in correlated queries, our algorithm produces diverse batches that enable efficient active learning at scale. We derive interpretable closed-form solutions akin to existing active learning procedures for linear models, and generalize to arbitrary models using random projections. We demonstrate the benefits of our approach on several large-scale regression and classification tasks.

To verify the effectiveness of PABEE on Computer Vision, we follow the experimental settings in Shallow-Deep [5], we conduct experiments on two image classification datasets, CIFAR-10 and CIFAR-100 [55]. We use ResNet-56 [10] as the backbone and compare PABEE with BranchyNet [26] and Shallow-Deep [5]. After every two convolutional layers, an internal classifier is added. We set the batch size to 128 and use SGD optimizer with learning rate of 0.1. Table 6: Experimental results (median of 5 runs) of ResNet based models on CIFAR-10 and CIFAR-100 datasets.

Score matching (SM) [24] provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bilevel optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

Reviewer 1: Thank you for the insightful analysis and acknowledgement of our effort. We will split the table to improve readability and test data. The model is clearly expressive enough as training and test accuracy are near-perfect. Reviewer 3: 1. XMC datasets have been well-researched and improvements "by couple of % points" are significant. In Sec 2.2 and Theorem 2.1, we rigorously showed the existence of a perfect accuracy For example, compare P@k and PSP@k of PfastreXML and FastXML in Table 3 and Table 4.

We present a novel probabilistic programming framework that couples directly to existing large-scale simulators through a cross-platform probabilistic execution protocol, which allows general-purpose inference engines to record and control random number draws within simulators in a language-agnostic way. The execution of existing simulators as probabilistic programs enables highly interpretable posterior inference in the structured model defined by the simulator code base. We demonstrate the technique in particle physics, on a scientifically accurate simulation of the τ (tau) lepton decay, which is a key ingredient in establishing the properties of the Higgs boson. Inference efficiency is achieved via inference compilation where a deep recurrent neural network is trained to parameterize proposal distributions and control the stochastic simulator in a sequential importance sampling scheme, at a fraction of the computational cost of a Markov chain Monte Carlo baseline.

Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges) scores. Given a generative model with an undirected connected graph G and true vector of binary labels y, it has been previously shown that when G has good expansion properties, such as complete graphs or d-regular expanders, one can exactly recover y (with high probability and in polynomial time) from a single noisy observation of each edge and node. We analyze the previously studied generative model by Globerson et al. (2015) under a notion of statistical parity. That is, given a fair binary node labeling, we ask the question whether it is possible to recover the fair assignment, with high probability and in polynomial time, from single edge and node observations. We find that, in contrast to the known trade-offs between fairness and model performance, the addition of the fairness constraint improves the probability of exact recovery. We effectively explain this phenomenon and empirically show how graphs with poor expansion properties, such as grids, are now capable of achieving exact recovery. Finally, as a byproduct of our analysis, we provide a tighter minimum-eigenvalue bound than that which can be derived from Weyl's inequality.