We introduce a new type of Deep Belief Net and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database(normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5% error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2% error, making it the current best result for NORB.

Neural activity is non-stationary and varies across time.

We present a simple new Monte Carlo algorithm for evaluating probabilities of observations in complex latent variable models, such as Deep Belief Networks. While the method is based on Markov chains, estimates based on short runs are formally unbiased. In expectation, the log probability of a test set will be underestimated, and this could form the basis of a probabilistic bound. The method is much cheaper than gold-standard annealing-based methods and only slightly more expensive than the cheapest Monte Carlo methods. We give examples of the new method substantially improving simple variational bounds at modest extra cost.

The worst-case complexity of general decentralized POMDPs, which are equivalent to partially observable stochastic games (POSGs) is very high, both for the cooperative and competitive cases. Some reductions in complexity have been achieved by exploiting independence relations in some models. We show that these results are somewhat limited: when these independence assumptions are relaxed in very small ways, complexity returns to that of the general case.

Offline handwriting recognition---the transcription of images of handwritten text---is an interesting task, in that it combines computer vision with sequence learning. In most systems the two elements are handled separately, with sophisticated preprocessing techniques used to extract the image features and sequential models such as HMMs used to provide the transcriptions. By combining two recent innovations in neural networks---multidimensional recurrent neural networks and connectionist temporal classification---this paper introduces a globally trained offline handwriting recogniser that takes raw pixel data as input. Unlike competing systems, it does not require any alphabet specific preprocessing, and can therefore be used unchanged for any language. Evidence of its generality and power is provided by data from a recent international Arabic recognition competition, where it outperformed all entries (91.4% accuracy compared to 87.2% for the competition winner) despite the fact that neither author understands a word of Arabic.

We propose a Bayesian nonparametric approach to relating multiple time series via a set of latent, dynamical behaviors. Using a beta process prior, we allow data-driven selection of the size of this set, as well as the pattern with which behaviors are shared among time series. Via the Indian buffet process representation of the beta process predictive distributions, we develop an exact Markov chain Monte Carlo inference method. In particular, our approach uses the sum-product algorithm to efficiently compute Metropolis-Hastings acceptance probabilities, and explores new dynamical behaviors via birth/death proposals. We validate our sampling algorithm using several synthetic datasets, and also demonstrate promising unsupervised segmentation of visual motion capture data.

Compressive Sensing (CS) combines sampling and compression into a single sub-Nyquist linear measurement process for sparse and compressible signals. In this paper, we extend the theory of CS to include signals that are concisely represented in terms of a graphical model. In particular, we use Markov Random Fields (MRFs) to represent sparse signals whose nonzero coefficients are clustered. Our new model-based reconstruction algorithm, dubbed Lattice Matching Pursuit (LaMP), stably recovers MRF-modeled signals using many fewer measurements and computations than the current state-of-the-art algorithms.

Continuous-time Markov chains are used to model systems in which transitions between states as well as the time the system spends in each state are random. Many computational problems related to such chains have been solved, including determining state distributions as a function of time, parameter estimation, and control. However, the problem of inferring most likely trajectories, where a trajectory is a sequence of states as well as the amount of time spent in each state, appears unsolved. We study three versions of this problem: (i) an initial value problem, in which an initial state is given and we seek the most likely trajectory until a given final time, (ii) a boundary value problem, in which initial and final states and times are given, and we seek the most likely trajectory connecting them, and (iii) trajectory inference under partial observability, analogous to finding maximum likelihood trajectories for hidden Markov models. We show that maximum likelihood trajectories are not always well-defined, and describe a polynomial time test for well-definedness. When well-definedness holds, we show that each of the three problems can be solved in polynomial time, and we develop efficient dynamic programming algorithms for doing so.

The Temporal Restricted Boltzmann Machine (TRBM) is a probabilistic model for sequences that is able to successfully model (i.e., generate nice-looking samples of) several very high dimensional sequences, such as motion capture data and the pixels of low resolution videos of balls bouncing in a box. The major disadvantage of the TRBM is that exact inference is extremely hard, since even computing a Gibbs update for a single variable of the posterior is exponentially expensive. This difficulty has necessitated the use of a heuristic inference procedure, that nonetheless was accurate enough for successful learning. In this paper we introduce the Recurrent TRBM, which is a very slight modification of the TRBM for which exact inference is very easy and exact gradient learning is almost tractable. We demonstrate that the RTRBM is better than an analogous TRBM at generating motion capture and videos of bouncing balls.

Discriminatively trained undirected graphical models have had wide empirical success, and there has been increasing interest in toolkits that ease their application to complex relational data. The power in relational models is in their repeated structure and tied parameters; at issue is how to define these structures in a powerful and flexible way. Rather than using a declarative language, such as SQL or first-order logic, we advocate using an imperative language to express various aspects of model structure, inference, and learning. By combining the traditional, declarative, statistical semantics of factor graphs with imperative definitions of their construction and operation, we allow the user to mix declarative and procedural domain knowledge, and also gain significant efficiencies. We have implemented such imperatively defined factor graphs in a system we call Factorie, a software library for an object-oriented, strongly-typed, functional language. In experimental comparisons to Markov Logic Networks on joint segmentation and coreference, we find our approach to be 3-15 times faster while reducing error by 20-25%-achieving a new state of the art.