Variational cross-validation of slow dynamical modes in molecular kinetics

Markov state models (MSMs) are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems. However, the lack of a unified theoretical framework for choosing between alternative models has hampered progress, especially for non-experts applying these methods to novel biological systems. Here, we consider cross-validation with a new objective function for estimators of these slow dynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-$m$ projection operator to capture the slow subspace of the system. It is shown that a variational theorem bounds the GMRQ from above by the sum of the first $m$ eigenvalues of the system's propagator, but that this bound can be violated when the requisite matrix elements are estimated subject to statistical uncertainty. This overfitting can be detected and avoided through cross-validation. These result make it possible to construct Markov state models for protein dynamics in a way that appropriately captures the tradeoff between systematic and statistical errors

Visual scene recognition with biologically relevant generative models

This research focuses on developing visual object categorization methodologies that are based on machine learning techniques and biologically inspired generative models of visual scene recognition. Modelling the statistical variability in visual patterns, in the space of features extracted from them by an appropriate low level signal processing technique, is an important matter of investigation for both humans and machines. To study this problem, we have examined in detail two recent probabilistic models of vision: a simple multivariate Gaussian model as suggested by (Karklin & Lewicki, 2009) and a restricted Boltzmann machine (RBM) proposed by (Hinton, 2002). Both the models have been widely used for visual object classification and scene analysis tasks before. This research highlights that these models on their own are not plausible enough to perform the classification task, and suggests Fisher kernel as a means of inducing discrimination into these models for classification power. Our empirical results on standard benchmark data sets reveal that the classification performance of these generative models could be significantly boosted near to the state of the art performance, by drawing a Fisher kernel from compact generative models that computes the data labels in a fraction of total computation time. We compare the proposed technique with other distance based and kernel based classifiers to show how computationally efficient the Fisher kernels are. To the best of our knowledge, Fisher kernel has not been drawn from the RBM before, so the work presented in the thesis is novel in terms of its idea and application to vision problem

Positive Definite Kernels in Machine Learning

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.Comment: draft. corrected a typo in figure

An Empirical Evaluation of Zero Resource Acoustic Unit Discovery

Acoustic unit discovery (AUD) is a process of automatically identifying a categorical acoustic unit inventory from speech and producing corresponding acoustic unit tokenizations. AUD provides an important avenue for unsupervised acoustic model training in a zero resource setting where expert-provided linguistic knowledge and transcribed speech are unavailable. Therefore, to further facilitate zero-resource AUD process, in this paper, we demonstrate acoustic feature representations can be significantly improved by (i) performing linear discriminant analysis (LDA) in an unsupervised self-trained fashion, and (ii) leveraging resources of other languages through building a multilingual bottleneck (BN) feature extractor to give effective cross-lingual generalization. Moreover, we perform comprehensive evaluations of AUD efficacy on multiple downstream speech applications, and their correlated performance suggests that AUD evaluations are feasible using different alternative language resources when only a subset of these evaluation resources can be available in typical zero resource applications.Comment: 5 pages, 1 figure; Accepted for publication at ICASSP 201

Multi-scale Discriminant Saliency with Wavelet-based Hidden Markov Tree Modelling

The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding classes . As the estimated discrepancy very much depends on considered scale level, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden Markov Tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, a saliency value for each square block at each scale level is computed with discriminant power principle. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multi-scale discriminant saliency (MDIS) method against the well-know information based approach AIM on its released image collection with eye-tracking data. Simulation results are presented and analysed to verify the validity of MDIS as well as point out its limitation for further research direction.Comment: arXiv admin note: substantial text overlap with arXiv:1301.396