We develop an inference and optimal design procedure for recovering synaptic weights in neural microcircuits. We base our procedure on data from an experiment in which populations of putative presynaptic neurons can be stimulated while a subthreshold recording is made from a single postsynaptic neuron. We present a realistic statistical model which accounts for the main sources of variability in this experiment and allows for large amounts of information about the biological system to be incorporated if available. We then present a simpler model to facilitate online experimental design which entails the use of efficient Bayesian inference. The optimized approach results in equal quality posterior estimates of the synaptic weights in roughly half the number of experimental trials under experimentally realistic conditions, tested on synthetic data generated from the full model.

Utilizing the structure of a probabilistic model can significantly increase its learning speed. Motivated by several recent applications, in particular bigram models in language processing, we consider learning low-rank conditional probability matrices under expected KL-risk. This choice makes smoothing, that is the careful handling of low-probability elements, paramount. We derive an iterative algorithm that extends classical non-negative matrix factorization to naturally incorporate additive smoothing and prove that it converges to the stationary points of a penalized empirical risk. We then derive sample-complexity bounds for the global minimizer of the penalized risk and show that it is within a small factor of the optimal sample complexity.

The most widely used technology to identify the proteins present in a complex biological sample is tandem mass spectrometry, which quickly produces a large collection of spectra representative of the peptides (i.e., protein subsequences) present in the original sample. In this work, we greatly expand the parameter learning capabilities of a dynamic Bayesian network (DBN) peptide-scoring algorithm, Didea, by deriving emission distributions for which its conditional log-likelihood scoring function remains concave. We show that this class of emission distributions, called Convex Virtual Emissions (CVEs), naturally generalizes the log-sum-exp function while rendering both maximum likelihood estimation and conditional maximum likelihood estimation concave for a wide range of Bayesian networks. Utilizing CVEs in Didea allows efficient learning of a large number of parameters while ensuring global convergence, in stark contrast to Didea's previous parameter learning framework (which could only learn a single parameter using a costly grid search) and other trainable models (which only ensure convergence to local optima). The newly trained scoring function substantially outperforms the state-of-the-art in both scoring function accuracy and downstream Fisher kernel analysis.

In large-scale applications of undirected graphical models, such as social networks and biological networks, similar patterns occur frequently and give rise to similar parameters. In this situation, it is beneficial to group the parameters for more efficient learning. We show that even when the grouping is unknown, we can infer these parameter groups during learning via a Bayesian approach. We impose a Dirichlet process prior on the parameters. Posterior inference usually involves calculating intractable terms, and we propose two approximation algorithms, namely a Metropolis-Hastings algorithm with auxiliary variables and a Gibbs sampling algorithm with stripped Beta approximation (Gibbs_SBA).

We propose a generalized Gibbs sampler algorithm for obtaining samples approximately distributed from a high-dimensional Gaussian distribution. Similarly to Hogwild methods, our approach does not target the original Gaussian distribution of interest, but an approximation to it. Contrary to Hogwild methods, a single parameter allows us to trade bias for variance. We show empirically that our method is very flexible and performs well compared to Hogwild-type algorithms. Papers published at the Neural Information Processing Systems Conference.

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian inference. Moreover, the optimization problem induces a new regularization for the posterior embedding estimator, which is faster and has comparable performance to the squared regularization in kernel Bayes' rule. This regularization coincides with a former thresholding approach used in kernel POMDPs whose consistency remains to be established. Our theoretical work solves this open problem and provides consistency analysis in regression settings.

This paper extends factorized asymptotic Bayesian (FAB) inference for latent feature models (LFMs). FAB inference has not been applicable to models, including LFMs, without a specific condition on the Hesqsian matrix of a complete log-likelihood, which is required to derive a factorized information criterion'' (FIC). Our asymptotic analysis of the Hessian matrix of LFMs shows that FIC of LFMs has the same form as those of mixture models. FAB/LFMs have several desirable properties (e.g., automatic hidden states selection and parameter identifiability) and empirically perform better than state-of-the-art Indian Buffet processes in terms of model selection, prediction, and computational efficiency." Papers published at the Neural Information Processing Systems Conference.

In sequential decision making, it is often important and useful for end users to understand the underlying patterns or causes that lead to the corresponding decisions. However, typical deep reinforcement learning algorithms seldom provide such information due to their black-box nature. In this paper, we present a probabilistic model, Q-LDA, to uncover latent patterns in text-based sequential decision processes. The model can be understood as a variant of latent topic models that are tailored to maximize total rewards; we further draw an interesting connection between an approximate maximum-likelihood estimation of Q-LDA and the celebrated Q-learning algorithm. We demonstrate in the text-game domain that our proposed method not only provides a viable mechanism to uncover latent patterns in decision processes, but also obtains state-of-the-art rewards in these games. Papers published at the Neural Information Processing Systems Conference.

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for matrix reconstruction. We have also successfully applied the proposed algorithm to a clustering problem, by formulating the problem of clustering as a low-rank matrix reconstruction problem with an additional structural property. Numerical experiments show that the proposed algorithm outperforms Lloyd's K-means algorithm.

Random projections have been increasingly adopted for a diverse set of tasks in machine learning involving dimensionality reduction. One specific line of research on this topic has investigated the use of quantization subsequent to projection with the aim of additional data compression. Motivated by applications in nearest neighbor search and linear learning, we revisit the problem of recovering inner products (respectively cosine similarities) in such setting. We show that even under coarse scalar quantization with 3 to 5 bits per projection, the loss in accuracy tends to range from negligible'' to moderate''. One implication is that in most scenarios of practical interest, there is no need for a sophisticated recovery approach like maximum likelihood estimation as considered in previous work on the subject.