The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$).

Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by including a discrete transformation variable. The resulting models perform clustering, dimensionality reduction and time-series analysis in a way that is invariant to transformations in the input. Using the EM algorithm, these transformation-invariant models can be fit to static data and time series. We give results on filtering microscopy images, face and facial pose clustering, handwritten digit modeling and recognition, video clustering, object tracking, and removal of distractions from video sequences.

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generalized mean field equations to optimize the cluster potentials. We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm. In addition, we address the problem of how to choose the graphical structure of the approximating distribution. From the generalised mean field equations we derive rules to simplify the structure of the approximating distribution in advance without affecting the quality of the approximation. We also show how the method fits into some other variational approximations that are currently popular.

We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity ininformation theory. We give astatistical analysis of the algorithm,bounding the number of samples requiredfor the stochastic algorithm to closelyapproximate the deterministic algorithmin each iteration. Simulations arepresented for several examples fromexponential families. Although we focuson applications to reference priors andminimax risk, the methods and analysiswe develop are applicable to a muchbroader class of optimization problemsand iterative algorithms.

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.

In the modern healthcare system, rapidly expanding costs/complexity, the growing myriad of treatment options, and exploding information streams that often do not effectively reach the front lines hinder the ability to choose optimal treatment decisions over time. The goal in this paper is to develop a general purpose (non-disease-specific) computational/artificial intelligence (AI) framework to address these challenges. This serves two potential functions: 1) a simulation environment for exploring various healthcare policies, payment methodologies, etc., and 2) the basis for clinical artificial intelligence - an AI that can think like a doctor. This approach combines Markov decision processes and dynamic decision networks to learn from clinical data and develop complex plans via simulation of alternative sequential decision paths while capturing the sometimes conflicting, sometimes synergistic interactions of various components in the healthcare system. It can operate in partially observable environments (in the case of missing observations or data) by maintaining belief states about patient health status and functions as an online agent that plans and re-plans. This framework was evaluated using real patient data from an electronic health record. Such an AI framework easily outperforms the current treatment-as-usual (TAU) case-rate/fee-for-service models of healthcare (Cost per Unit Change: $189 vs. $497) while obtaining a 30-35% increase in patient outcomes. Tweaking certain model parameters further enhances this advantage, obtaining roughly 50% more improvement for roughly half the costs. Given careful design and problem formulation, an AI simulation framework can approximate optimal decisions even in complex and uncertain environments. Future work is described that outlines potential lines of research and integration of machine learning algorithms for personalized medicine.

We propose a new approach to value-directed belief state approximation for POMDPs. The value-directed model allows one to choose approximation methods for belief state monitoring that have a small impact on decision quality. Using a vector space analysis of the problem, we devise two new search procedures for selecting an approximation scheme that have much better computational properties than existing methods. Though these provide looser error bounds, we show empirically that they have a similar impact on decision quality in practice, and run up to two orders of magnitude more quickly.

We consider a partially observable Markov decision problem (POMDP) that models a class of sequencing problems. Although POMDPs are typically intractable, our formulation admits tractable solution. Instead of maintaining a value function over a high-dimensional set of belief states, we reduce the state space to one of smaller dimension, in which grid-based dynamic programming techniques are effective. We develop an error bound for the resulting approximation, and discuss an application of the model to a problem in targeted advertising.

We present a new method for estimating the expected return of a POMDP from experience. The method does not assume any knowledge of the POMDP and allows the experience to be gathered from an arbitrary sequence of policies. The return is estimated for any new policy of the POMDP. We motivate the estimator from function-approximation and importance sampling points-of-view and derive its theoretical properties. Although the estimator is biased, it has low variance and the bias is often irrelevant when the estimator is used for pair-wise comparisons. We conclude by extending the estimator to policies with memory and compare its performance in a greedy search algorithm to REINFORCE algorithms showing an order of magnitude reduction in the number of trials required.

Automatic continuous speech recognition (CSR) is sufficiently mature that a variety of real world applications are now possible including large vocabulary transcription and interactive spoken dialogues. This paper reviews the evolution of the statistical modelling techniques which underlie current-day systems, specifically hidden Markov models (HMMs) and N-grams. Starting from a description of the speech signal and its parameterisation, the various modelling assumptions and their consequences are discussed. It then describes various techniques by which the effects of these assumptions can be mitigated. Despite the progress that has been made, the limitations of current modelling techniques are still evident. The paper therefore concludes with a brief review of some of the more fundamental modelling work now in progress.