Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient algorithm for sampling based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required cannot be directly extended except in a few restricted cases. In this paper, we present efficient approximate DPP sampling schemes based on Nystrom and random Fourier feature approximations that apply to a wide range of kernel functions. We demonstrate the utility of continuous DPPs in repulsive mixture modeling applications and synthesizing human poses spanning activity spaces.

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.

Computing the stationary distribution of a large finite or countably infinite state space Markov Chain (MC) has become central in many problems such as statistical inference and network analysis. Standard methods involve large matrix multiplications as in power iteration, or simulations of long random walks to sample states from the stationary distribution, as in Markov Chain Monte Carlo (MCMC). However these methods are computationally costly; either they involve operations at every state or they scale (in computation time) at least linearly in the size of the state space. In this paper, we provide a novel algorithm that answers whether a chosen state in a MC has stationary probability larger than some $\Delta \in (0,1)$. If so, it estimates the stationary probability. Our algorithm uses information from a local neighborhood of the state on the graph induced by the MC, which has constant size relative to the state space. We provide correctness and convergence guarantees that depend on the algorithm parameters and mixing properties of the MC. Simulation results show MCs for which this method gives tight estimates.

Many machine learning problems can be interpreted as learning for matching two types of objects (e.g., images and captions, users and products, queries and documents). The matching level of two objects is usually measured as the inner product in a certain feature space, while the modeling effort focuses on mapping of objects from the original space to the feature space. This schema, although proven successful on a range of matching tasks, is insufficient for capturing the rich structure in the matching process of more complicated objects. In this paper, we propose a new deep architecture to more effectively model the complicated matching relations between two objects from heterogeneous domains. More specifically, we apply this model to matching tasks in natural language, e.g., finding sensible responses for a tweet, or relevant answers to a given question. This new architecture naturally combines the localness and hierarchy intrinsic to the natural language problems, and therefore greatly improves upon the state-of-the-art models.

We introduce a novel formulation of multi-task learning (MTL) called parametric task learning (PTL) that can systematically handle infinitely many tasks parameterized by a continuous parameter. Our key finding is that, for a certain class of PTL problems, the path of optimal task-wise solutions can be represented as piecewise-linear functions of the continuous task parameter. Based on this fact, we employ a parametric programming technique to obtain the common shared representation across all the continuously parameterized tasks efficiently. We show that our PTL formulation is useful in various scenarios such as learning under non-stationarity, cost-sensitive learning, and quantile regression, and demonstrate the usefulness of the proposed method experimentally in these scenarios.

We investigate the problem of learning the structure of a Markov network from data. It is shown that the structure of such networks can be described in terms of constraints which enables the use of existing solver technology with optimization capabilities to compute optimal networks starting from initial scores computed from the data. To achieve efficient encodings, we develop a novel characterization of Markov network structure using a balancing condition on the separators between cliques forming the network. The resulting translations into propositional satisfiability and its extensions such as maximum satisfiability, satisfiability modulo theories, and answer set programming, enable us to prove the optimality of networks which have been previously found by stochastic search.

Sparse high-dimensional data vectors are common in many application domains where a very large number of rarely non-zero features can be devised. Unfortunately, this creates a computational bottleneck for unsupervised feature learning algorithms such as those based on auto-encoders and RBMs, because they involve a reconstruction step where the whole input vector is predicted from the current feature values. An algorithm was recently developed to successfully handle the case of auto-encoders, based on an importance sampling scheme stochastically selecting which input elements to actually reconstruct during training for each particular example. To generalize this idea to RBMs, we propose a stochastic ratio-matching algorithm that inherits all the computational advantages and unbiasedness of the importance sampling scheme. We show that stochastic ratio matching is a good estimator, allowing the approach to beat the state-of-the-art on two bag-of-word text classification benchmarks (20 Newsgroups and RCV1), while keeping computational cost linear in the number of non-zeros.

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.