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Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
Semantic segmentation aims to robustly predict coherent class labels for entire regions of an image. It is a scene understanding task that powers real-world applications (e.g., autonomous navigation). One important application, the use of…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are…
Tracking the kinematics of fast-moving objects is an important diagnostic tool for science and engineering. Existing optical methods include high-speed CCD/CMOS imaging, streak cameras, lidar, serial time-encoded imaging and sequentially…
We present a novel method for accurate and efficient up- sampling of sparse depth data, guided by high-resolution imagery. Our approach goes beyond the use of intensity cues only and additionally exploits object boundary cues through…
This EM review article focuses on parameter expansion, a simple technique introduced in the PX-EM algorithm to make EM converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between…
Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…
This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
The estimation of the ratio of two density probability functions is of great interest in many statistics fields, including causal inference. In this study, we develop an ensemble estimator of density ratios with a novel loss function based…
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman…
Suppose that we wish to estimate a finite-dimensional summary of one or more function-valued features of an underlying data-generating mechanism under a nonparametric model. One approach to estimation is by plugging in flexible estimates of…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we…
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…