Adaptive Approximation of Shapes

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This thesis deals with exploiting the low-dimensional multi-subspace structure of speech towards the goal of improving acoustic modeling for automatic speech recognition (ASR). Leveraging the parsimonious hierarchical nature of speech, we hypothesize that ...

Towards the goal of improving acoustic modeling for automatic speech recognition (ASR), this work investigates the modeling of senone subspaces in deep neural network (DNN) posteriors using low-rank and sparse modeling approaches. While DNN posteriors are ...

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

rate of convergence for the squared norm of the gradient of Moreau envelope, ...

We propose a noise robust two-step phase shifting algorithm for the evaluation of random and unknown phase step. In this algorithm, the phase within a small size two-dimensional window around a user selected pixel in an interferogram is approximated as a q ...

Background: For the functional control of prosthetic hand, it is insufficient to obtain only the motion pattern information. As far as practicality is concerned, the control of the prosthetic hand force is indispensable. The application value of prosthetic ...

The focus of this thesis is to develop methods to address research challenges related to correlation patterns in discrete choice models. In the context of correlations within alternatives, we extend the novel methodology of the multiple indicator solution ...

Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the development of a ...

Independent Component Analysis (ICA) has proven to be an effective data driven method for analyzing EEG data, separating signals from temporally and functionally independent brain and non-brain source processes and thereby increasing their definition. Dime ...

We showthat any k-th closed sphere-of-influence graph in a d-dimensional normed space has a vertex of degree less than 5dk, thus obtaining a common generalization of results of Furedi and Loeb (Proc AmMath Soc 121(4): 1063-1073, 1994 [1]) and Guibas et al. ...

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS ...

Next-generation radio-interferometers face a computing challenge with respect to the imaging techniques that can be applied in the big data setting in which they are designed. Dimensionality reduction can thus provide essential savings of computing resourc ...

The Cartan formula encodes the relationship between the cup product and the action of the Steenrod algebra in F-p-cohomology. In this work, we present an effective proof of the Cartan formula at the cochain level when the field is F-2. More explicitly, for ...

The number of materials or molecules that can be created by combining different chemical elements in various proportions and spatial arrangements is enormous. Computational chemistry can be used to generate databases containing billions of potential struct ...

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging method ...

The amount of data that we produce and consume is larger than it has been at any point in the history of mankind, and it keeps growing exponentially. All this information, gathered in overwhelming volumes, often comes with two problematic characteristics: ...

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...

Adaptive Approximation of Shapes

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Sparse and Low-rank Modeling for Automatic Speech Recognition

Low-rank and sparse subspace modeling of speech for DNN based acoustic modeling

Convex optimization in sums of Banach spaces

Convergence of adaptive algorithms for constrained weakly convex optimization

Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

PCA and deep learning based myoelectric grasping control of a prosthetic hand

Dealing with Correlations in Discrete Choice Models

High Dimensional Bayesian Optimization via Additive Models with Overlapping Groups

Applying dimension reduction to EEG data by Principal Component Analysis reduces the quality of its subsequent Independent Component decomposition

Sphere-of-Influence Graphs in Normed Spaces

Linear credit risk models

Fourier dimensionality reduction of radio-interferometric data

An effective proof of the Cartan formula: The even prime

Chemiscope: interactive structure-property explorer for materials and molecules

A Fourier dimensionality reduction model for big data interferometric imaging

Graph-based Methods for Visualization and Clustering

A Unifying Representer Theorem for Inverse Problems and Machine Learning

On long time behavior of solutions to nonlinear dispersive equations