Maximum entropy inverse optimal control (MaxEnt IOC) is an effective means of discovering the underlying cost function of demonstrated human activity and can be used to predict human behavior over low-dimensional state spaces (i.e., forecasting of 2D trajectories). To enable inference in very large state spaces, we introduce an approximate MaxEnt IOC procedure to address the fundamental computational bottleneck stemming from calculating the partition function via dynamic programming. Approximate MaxEnt IOC is based on two components: approximate dynamic programming and Monte Carlo sampling. We analyze this approximation approach and provide a finite-sample error upper bound on its excess loss. We validate the proposed method in the context of analyzing dual-agent interactions from video, where we use approximate MaxEnt IOC to simulate mental images of a single agents body pose sequence (a high-dimensional image space). We experiment with sequences image data taken from RGB and RGBD data and show that it is possible to learn cost functions that lead to accurate predictions in high-dimensional problems that were previously intractable.

Word Sense Disambiguation is a difficult problem to solve in the unsupervised setting. This is because in this setting inference becomes more dependent on the interplay between different senses in the context due to unavailability of learning resources. Using two basic ideas, sense dependency and selective dependency, we model the WSD problem as a Maximum A Posteriori (MAP) Inference Query on a Markov Random Field (MRF) built using WordNet and Link Parser or Stanford Parser. To the best of our knowledge this combination of dependency and MRF is novel, and our graph-based unsupervised WSD system beats state-of-the-art system on SensEval-2, SensEval-3 and SemEval-2007 English all-words datasets while being over 35 times faster.

Most previous work on video description trains individualparts of speech independently. It is more appealing from a linguistic point of view, for word models for all parts of speech to be learned simultaneously from whole sentences, a hypothesis suggested by some linguists for child language acquisition. In this paper, we learn to describe video by discriminatively training positive sentential labels against negative ones in a weakly supervised fashion: the meaning representations (i.e., HMMs) of individual words in these labels are learned from whole sentences without any correspondence annotation of what those words denote in the video. Textual descriptions are then generated for new video using trained word models.

A key challenge in the design of multi-sensor systems is the efficient allocation of scarce resources such as bandwidth, CPU cycles, and energy, leading to the dynamic sensor selection problem in which a subset of the available sensors must be selected at each timestep. While partially observable Markov decision processes (POMDPs) provide a natural decision-theoretic model for this problem, the computational cost of POMDP planning grows exponentially in the number of sensors, making it feasible only for small problems. We propose a new POMDP planning method that uses greedy maximization to greatly improve scalability in the number of sensors. We show that, under certain conditions, the value function of a dynamic sensor selection POMDP is submodular and use this result to bound the error introduced by performing greedy maximization. Experimental results on a real-world dataset from a multi-camera tracking system in a shopping mall show it achieves similar performance to existing methods but incurs only a fraction of the computational cost, leading to much better scalability in the number of cameras.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

The global financial crisis occurred in 2008 and its contagion to other regions, as well as the long-lasting impact on different markets, show that it is increasingly important to understand the complicated coupling relationships across financial markets. This is indeed very difficult as complex hidden coupling relationships exist between different financial markets in various countries, which are very hard to model. The couplings involve interactions between homogeneous markets from various countries (we call intra-market coupling), interactions between heterogeneous markets (inter-market coupling) and interactions between current and past market behaviors (temporal coupling). Very limited work has been done towards modeling such complex couplings, whereas some existing methods predict market movement by simply aggregating indicators from various markets but ignoring the inbuilt couplings. As a result, these methods are highly sensitive to observations, and may often fail when financial indicators change slightly. In this paper, a coupled deep belief network is designed to accommodate the above three types of couplings across financial markets. With a deep-architecture model to capture the high-level coupled features, the proposed approach can infer market trends. Experimental results on data of stock and currency markets from three countries show that our approach outperforms other baselines, from both technical and business perspectives.

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning Multivariate Time Series (MTS). However, in general, it is difficult to set the dimension of an LDS's hidden state space. A small number of hidden states may not be able to model the complexities of a MTS, while a large number of hidden states can lead to overfitting. In this paper, we study learning methods that impose various regularization penalties on the transition matrix of the LDS model and propose a regularized LDS learning framework (rLDS) which aims to (1) automatically shut down LDSs' spurious and unnecessary dimensions, and consequently, address the problem of choosing the optimal number of hidden states; (2) prevent the overfitting problem given a small amount of MTS data; and (3) support accurate MTS forecasting. To learn the regularized LDS from data we incorporate a second order cone program and a generalized gradient descent method into the Maximum a Posteriori framework and use Expectation Maximization to obtain a low-rank transition matrix of the LDS model. We propose two priors for modeling the matrix which lead to two instances of our rLDS. We show that our rLDS is able to recover well the intrinsic dimensionality of the time series dynamics and it improves the predictive performance when compared to baselines on both synthetic and real-world MTS datasets.

Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

Planning in large partially observable Markov decision processes (POMDPs) is challenging especially when a long planning horizon is required. A few recent algorithms successfully tackle this case but at the expense of a weaker information-gathering capacity. In this paper, we propose Information Gathering and Reward Exploitation of Subgoals (IGRES), a randomized POMDP planning algorithm that leverages information in the state space to automatically generate "macro-actions" to tackle tasks with long planning horizons, while locally exploring the belief space to allow effective information gathering. Experimental results show that IGRES is an effective multi-purpose POMDP solver, providing state-of-the-art performance for both long horizon planning tasks and information-gathering tasks on benchmark domains. Additional experiments with an ecological adaptive management problem indicate that IGRES is a promising tool for POMDP planning in real-world settings.

Markov logic networks (MLNs) combine the power of first-order logic and probabilistic graphical models and as a result are ideally suited for solving large, complex problems in application domains that have both rich relational structure and large amount of uncertainty. However, inference in these rich, relational representations is quite challenging. The aim of this thesis is to advance the state-of-the-art in MLN inference, enabling it to solve much harder and more complex tasks than is possible today. To this end, I will develop techniques that exploit logical structures and symmetries that are either explicitly or implicitly encoded in the MLN representation and demonstrate their usefulness by using them to solve hard real-world problems in the field of natural language understanding.