Auxiliary variational MCMC

We introduce Auxiliary Variational MCMC, a novel framework for learning MCMC kernels that combines recent advances in variational inference with insights drawn from traditional auxiliary variable MCMC methods such as Hamiltonian Monte Carlo. Our framework exploits low dimensional structure in the target distribution in order to learn a more efficient MCMC sampler. The resulting sampler is able to suppress random walk behaviour and mix between modes efficiently, without the need to compute gradients of the target distribution. We test our sampler on a number of challenging distributions, where the underlying structure is known, and on the task of posterior sampling in Bayesian logistic regression. Code to reproduce all experiments is available at https://github.com/AVMCMC

Robust and Efficient Inference of Scene and Object Motion in Multi-Camera Systems

Multi-camera systems have the ability to overcome some of the fundamental limitations of single camera based systems. Having multiple view points of a scene goes a long way in limiting the influence of field of view, occlusion, blur and poor resolution of an individual camera. This dissertation addresses robust and efficient inference of object motion and scene in multi-camera and multi-sensor systems. The first part of the dissertation discusses the role of constraints introduced by projective imaging towards robust inference of multi-camera/sensor based object motion. We discuss the role of the homography and epipolar constraints for fusing object motion perceived by individual cameras. For planar scenes, the homography constraints provide a natural mechanism for data association. For scenes that are not planar, the epipolar constraint provides a weaker multi-view relationship. We use the epipolar constraint for tracking in multi-camera and multi-sensor networks. In particular, we show that the epipolar constraint reduces the dimensionality of the state space of the problem by introducing a ``shared'' state space for the joint tracking problem. This allows for robust tracking even when one of the sensors fail due to poor SNR or occlusion. The second part of the dissertation deals with challenges in the computational aspects of tracking algorithms that are common to such systems. Much of the inference in the multi-camera and multi-sensor networks deal with complex non-linear models corrupted with non-Gaussian noise. Particle filters provide approximate Bayesian inference in such settings. We analyze the computational drawbacks of traditional particle filtering algorithms, and present a method for implementing the particle filter using the Independent Metropolis Hastings sampler, that is highly amenable to pipelined implementations and parallelization. We analyze the implementations of the proposed algorithm, and in particular concentrate on implementations that have minimum processing times. The last part of the dissertation deals with the efficient sensing paradigm of compressing sensing (CS) applied to signals in imaging, such as natural images and reflectance fields. We propose a hybrid signal model on the assumption that most real-world signals exhibit subspace compressibility as well as sparse representations. We show that several real-world visual signals such as images, reflectance fields, videos etc., are better approximated by this hybrid of two models. We derive optimal hybrid linear projections of the signal and show that theoretical guarantees and algorithms designed for CS can be easily extended to hybrid subspace-compressive sensing. Such methods reduce the amount of information sensed by a camera, and help in reducing the so called data deluge problem in large multi-camera systems

Acoustic node calibration using moving sources

Acoustic nodes, each containing an array of microphones, can track targets in x-y space from their received acoustic signals, if the node positions and orientations are known exactly. However, it is not always possible to deploy the nodes precisely, so a calibration phase is needed to estimate the position and the orientation of each node before doing any tracking or localization. An acoustic node can be calibrated from sources of opportunity such as beacons or a moving source. In this paper, we derive and compare several calibration methods for the case where the node can hear a moving source whose position can be reported back to the node. Since calibration from a moving source is, in effect, the dual of a tracking problem, methods derived for acoustic target trackers are used to obtain robust and high resolution acoustic calibration processes. For example, two direction-of-arrival-based calibration methods can be formulated based on combining angle estimates, geometry, and the motion dynamics of the moving source. In addition, a maximum-likelihood (ML) solution is presented using a narrow-band acoustic observation model, along with a Newton-based search algorithm that speeds up the calculation the likelihood surface. The Cramer-Rao lower bound on the node position estimates is also derived to show that the effect of position errors for the moving source on the estimated node position is much less severe than the variance in angle estimates from the microphone array. The performance of the calibration algorithms is demonstrated on synthetic and field data

Advances in Probabilistic Deep Learning

This thesis is concerned with methodological advances in probabilistic inference and their application to core challenges in machine perception and AI. Inferring a posterior distribution over the parameters of a model given some data is a central challenge that occurs in many fields ranging from finance and artificial intelligence to physics. Exact calculation is impossible in all but the simplest cases and a rich field of approximate inference has been developed to tackle this challenge. This thesis develops both an advance in approximate inference and an application of these methods to the problem of speech synthesis. In the first section of this thesis we develop a novel framework for constructing Markov Chain Monte Carlo (MCMC) kernels that can efficiently sample from high dimensional distributions such as the posteriors, that frequently occur in machine perception. We provide a specific instance of this framework and demonstrate that it can match or exceed the performance of Hamiltonian Monte Carlo without requiring gradients of the target distribution. In the second section of the thesis we focus on the application of approximate inference techniques to the task of synthesising human speech from text. By using advances in neural variational inference we are able to construct a state of the art speech synthesis system in which it is possible to control aspects of prosody such as emotional expression from significantly less supervised data than previously existing state of the art methods

Acoustic node calibration using helicopter sounds and Monte Carlo markov chain methods

A Monte-Carlo method is used to calibrate a randomly placed sensor node using helicopter sounds. The calibration is based on using the GPS information from the helicopter and the estimated DOA's at the node. The related Cramer-Rao lower bound is derived and the effects of the GPS errors on the position estimates are derived. Issues related to the processing of the field data, e.g., time synchronization and data nonstationarity are discussed. The effects of the GPS errors are shown to be negligible under certain conditions. Finally, the results of the calibration on field data are given

Active search in intensionally specified structured spaces

We consider an active search problem in intensionally specified structured spaces. The ultimate goal in this setting is to discover structures from structurally different partitions of a fixed but unknown target class. An example of such a process is that of computer-aided de novo drug design. In the past 20 years several Monte Carlo search heuristics have been developed for this process. Motivated by these hand-crafted search heuristics, we devise a Metropolis--Hastings sampling scheme where the acceptance probability is given by a probabilistic surrogate of the target property, modeled with a max entropy conditional model. The surrogate model is updated in each iteration upon the evaluation of a selected structure. The proposed approach is consistent and the empirical evidence indicates that it achieves a large structural variety of discovered targets

Bayesian sparse Fourier representation of off-grid targets with application to experimental radar data

The problem considered is the estimation of a finite number of cisoids embedded in white noise, using a sparse signal representation (SSR) approach, a problem which is relevant in many radar applications. Many SSR algorithms have been developed in order to solve this problem, but they usually are sensitive to grid mismatch. In this paper, two Bayesian algorithms are presented, which are robust towards grid mismatch: a first method uses a Fourier dictionary directly parametrized by the grid mismatch while the second one employs a first-order Taylor approximation to relate linearly the grid mismatch and the sparse vector. The main strength of these algorithms lies in the use of a mixed-type distribution which decorrelates sparsity level and target power. Besides, both methods are implemented through a Monte-Carlo Markov chain algorithm. They are successfully evaluated on synthetic and experimental radar data, and compared to a benchmark algorith