Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parametrized by interaction weights and biases. We address the representational power of these models, proving results their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.

We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is $L_1$ regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. $L_1$ regularization impedes the simple application of the gradient method, which optimizes the cost function that leads to accurate estimations, owing to the cost function's lack of smoothness. In this study, we utilize the majorizer minimization method, which is a well-known technique implemented in optimization problems, to avoid the non-smoothness of the cost function. By using the majorizer minimization method, we elucidate essentially relevant biases and interactions from given data with seemingly strongly-correlated components.

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.

We study the problem of learning sparse structure changes between two Markov networks P and Q. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn changes directly via estimating the ratio between two Markov network models.  Such a direct approach was demonstrated to perform excellently in experiments, although its theoretical properties remained unexplored.  In this paper, we give sufficient conditions for successful change detection with respect to the sample size np, nq, the dimension of data m, and the number of changed edges d.

While probabilistic planning models have been extensively used by AI and Decision Theoretic communities for planning under uncertainty, the objective to minimize the expected cumulative cost is inappropriate for high-stake planning problems. With this motivation in mind, we revisit the Risk-Sensitive criterion (RS-criterion), where the objective is to find a policy that maximizes the probability that the cumulative cost is within some user-defined cost threshold. The overall scope of this research is to develop efficient and scalable algorithms to optimize the RS-criterion in probabilistic planning problems. In our recent paper (Hou, Yeoh, and Varakantham 2014), we formally defined Risk-Sensitive MDPs (RS-MDPs) and introduced new algorithms for RS-MDPs with non-negative costs. Next, my plan is to develop algorithm for RS-MDPs with negative cost cycles and for Risk-Sensitive POMDPs (RS-POMDPs).

The classical planning problem can be enriched with quantitative and qualitative user-defined preferences on how the system behaves on achieving the goal. In this paper, we propose the probabilistic preference planning problem for Markov decision processes, where the preferences are based on an enriched probabilistic LTL-style logic. We develop P4Solver, an SMT-based planner computing the preferred plan by reducing the problem to quadratic programming problem, which can be solved using SMT solvers such as Z3. We illustrate the framework by applying our approach on two selected case studies.

Documents from the same domain usually discuss similar topics in a similar order. However, the number of topics and the exact topics discussed in each individual document can vary. In this paper we present a simple topic model that uses generalised Mallows models and incomplete topic orderings to incorporate this ordering regularity into the probabilistic generative process of the new model. We show how to reparameterise the new model so that a point-wise sampling algorithm from the Bayesian word segmentation literature can be used for inference. This algorithm jointly samples not only the topic orders and the topic assignments but also topic segmentations of documents. Experimental results show that our model performs significantly better than the other ordering-based topic models on nearly all the corpora that we used, and competitively with other state-of-the-art topic segmentation models on corpora that have a strong ordering regularity.

Faced with the problem of characterizing systematic changes in multivariate time series in an unsupervised manner, we derive and test two methods of regularizing hidden Markov models for this task. Regularization on state transitions provides smooth transitioning among states, such that the sequences are split into broad, contiguous segments. Our methods are compared with a recent hierarchical Dirichlet process hidden Markov model (HDP-HMM) and a baseline standard hidden Markov model, of which the former suffers from poor performance on moderate-dimensional data and sensitivity to parameter settings, while the latter suffers from rapid state transitioning, over-segmentation and poor performance on a segmentation task involving human activity accelerometer data from the UCI Repository. The regularized methods developed here are able to perfectly characterize change of behavior in the human activity data for roughly half of the real-data test cases, with accuracy of 94% and low variation of information. In contrast to the HDP-HMM, our methods provide simple, drop-in replacements for standard hidden Markov model update rules, allowing standard expectation maximization (EM) algorithms to be used for learning.

In this paper, we consider the problem of energy disaggregation, i.e., decomposing a whole home electricity signal into its component appliances. We propose a new supervised algorithm, which in the learning stage, automatically extracts signature consumption patterns of each device by modeling the device as a mixture of dynamical systems. In order to extract signature consumption patterns of a device corresponding to its different modes of operation, we define appropriate dissimilarities between energy snippets of the device and use them in a subset selection scheme, which we generalize to deal with time-series data. We then form a dictionary that consists of extracted power signatures across all devices. We cast the disaggregation problem as an optimization over a representation in the learned dictionary and incorporate several novel priors such as device-sparsity, knowledge about devices that do or do not work together as well as temporal consistency of the disaggregated solution. Real experiments on a publicly available energy dataset demonstrate that our proposed algorithm achieves promising results for energy disaggregation.

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.