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Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
In this work, we propose an extension of conventional image data by an additional channel in which the associated projection properties are encoded. This addresses the issue of sensor-dependent object representation in projection-based…
In this paper, we address the problem of classifying data within the radar reference window in terms of statistical properties. Specifically, we partition these data into statistically homogeneous subsets by identifying possible clutter…
Realtime shape estimation of continuum objects and manipulators is essential for developing accurate planning and control paradigms. The existing methods that create dense point clouds from camera images, and/or use distinguishable markers…
Sequential Latin hypercube designs have recently received great attention for computer experiments. Much of the work has been restricted to invariant spaces. The related systematic construction methods are inflexible while algorithmic…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
A common challenge in computer experiments and related fields is to efficiently explore the input space using a small number of samples, i.e., the experimental design problem. Much of the recent focus in the computer experiment literature,…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
One-shot decision making is required in situations in which we can evaluate a fixed number of solution candidates but do not have any possibility for further, adaptive sampling. Such settings are frequently encountered in neural network…
This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for…
Many data analysis problems can be cast as distance geometry problems in \emph{space forms} -- Euclidean, spherical, or hyperbolic spaces. Often, absolute distance measurements are often unreliable or simply unavailable and only proxies to…
Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…
In computer experiments, it has become a standard practice to select the inputs that spread out as uniformly as possible over the design space. The resulting designs are called space-filling designs and they are undoubtedly desirable…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…
A computer model can be used for predicting an output only after specifying the values of some unknown physical constants known as calibration parameters. The unknown calibration parameters can be estimated from real data by conducting…