We propose a new class of structured Schatten norms for tensors that includes two recently proposed norms (overlapped'' and "latent'') for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we mathematically analyze the performance of "latent'' approach for tensor decomposition, which was empirically found to perform better than the "overlapped'' approach in some settings. We show theoretically that this is indeed the case. In particular, when the unknown true tensor is low-rank in a specific mode, this approach performs as well as knowing the mode with the smallest rank. Along the way, we show a novel duality result for structures Schatten norms, which is also interesting in the general context of structured sparsity. We confirm through numerical simulations that our theory can precisely predict the scaling behaviour of the mean squared error. "

Stochastic And-Or grammars compactly represent both compositionality and reconfigurability and have been used to model different types of data such as images and events. We present a unified formalization of stochastic And-Or grammars that is agnostic to the type of the data being modeled, and propose an unsupervised approach to learning the structures as well as the parameters of such grammars. Starting from a trivial initial grammar, our approach iteratively induces compositions and reconfigurations in a unified manner and optimizes the posterior probability of the grammar. In our empirical evaluation, we applied our approach to learning event grammars and image grammars and achieved comparable or better performance than previous approaches.

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.

In visual recognition problems, the common data distribution mismatches between training and testing make domain adaptation essential. However, image data is difficult to manually divide into the discrete domains required by adaptation algorithms, and the standard practice of equating datasets with domains is a weak proxy for all the real conditions that alter the statistics in complex ways (lighting, pose, background, resolution, etc.) We propose an approach to automatically discover latent domains in image or video datasets. Our formulation imposes two key properties on domains: maximum distinctiveness and maximum learnability. By maximum distinctiveness, we require the underlying distributions of the identified domains to be different from each other; by maximum learnability, we ensure that a strong discriminative model can be learned from the domain. We devise a nonparametric representation and efficient optimization procedure for distinctiveness, which, when coupled with our learnability constraint, can successfully discover domains among both training and test data. We extensively evaluate our approach on object recognition and human activity recognition tasks.

We address the problem of deciding whether there exists a consistent estimator of a given relation Q, when data are missing not at random. We employ a formal representation called `Missingness Graphs' to explicitly portray the causal mechanisms responsible for missingness and to encode dependencies between these mechanisms and the variables being measured. Using this representation, we define the notion of \textit{recoverability} which ensures that, for a given missingness-graph $G$ and a given query $Q$ an algorithm exists such that in the limit of large samples, it produces an estimate of $Q$ \textit{as if} no data were missing. We further present conditions that the graph should satisfy in order for recoverability to hold and devise algorithms to detect the presence of these conditions.

We propose a compressed sensing (CS) calcium imaging framework for monitoring large neuronal populations, where we image randomized projections of the spatial calcium concentration at each timestep, instead of measuring the concentration at individual locations. We develop scalable nonnegative deconvolution methods for extracting the neuronal spike time series from such observations. We also address the problem of demixing the spatial locations of the neurons using rank-penalized matrix factorization methods. By exploiting the sparsity of neural spiking we demonstrate that the number of measurements needed per timestep is significantly smaller than the total number of neurons, a result that can potentially enable imaging of larger populations at considerably faster rates compared to traditional raster-scanning techniques. Unlike traditional CS setups, our problem involves a block-diagonal sensing matrix and a non-orthogonal sparse basis that spans multiple timesteps. We study the effect of these distinctive features in a noiseless setup using recent results relating conic geometry to CS. We provide tight approximations to the number of measurements needed for perfect deconvolution for certain classes of spiking processes, and show that this number displays a phase transition," similar to phenomena observed in more standard CS settings; however, in this case the required measurement rate depends not just on the mean sparsity level but also on other details of the underlying spiking process."

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). Simulations show that both algorithms outperform conventional maximum likelihood estimation (MLE). Gibbs_SBA's performance is close to Gibbs sampling with exact likelihood calculation. Models learned with Gibbs_SBA also generalize better than the models learned by MLE on real-world Senate voting data.

We propose a parameter server system for distributed ML, which follows a Stale Synchronous Parallel (SSP) model of computation that maximizes the time computational workers spend doing useful work on ML algorithms, while still providing correctness guarantees. The parameter server provides an easy-to-use shared interface for read/write access to an ML model's values (parameters and variables), and the SSP model allows distributed workers to read older, stale versions of these values from a local cache, instead of waiting to get them from a central storage. This significantly increases the proportion of time workers spend computing, as opposed to waiting. Furthermore, the SSP model ensures ML algorithm correctness by limiting the maximum age of the stale values. We provide a proof of correctness under SSP, as well as empirical results demonstrating that the SSP model achieves faster algorithm convergence on several different ML problems, compared to fully-synchronous and asynchronous schemes.

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."

Structure learning algorithms for graphical models have focused almost exclusively on stable environments in which the underlying generative process does not change; that is, they assume that the generating model is globally stationary. In real-world environments, however, such changes often occur without warning or signal. Real-world data often come from generating models that are only locally stationary. In this paper, we present LoSST, a novel, heuristic structure learning algorithm that tracks changes in graphical model structure or parameters in a dynamic, real-time manner. We show by simulation that the algorithm performs comparably to batch-mode learning when the generating graphical structure is globally stationary, and significantly better when it is only locally stationary.