Related papers: Probabilistic classifiers with low rank indefinite…

Selecting important features in non-linear or kernel spaces is a difficult challenge in both classification and regression problems. When many of the features are irrelevant, kernel methods such as the support vector machine and kernel…

Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…

We present a computational framework for piecewise constant functions (PCFs) and use this for several types of computations that are useful in statistics, e.g., averages, similarity matrices, and so on. We give a linear-time,…

We consider the problem of learning predictive models from longitudinal data, consisting of irregularly repeated, sparse observations from a set of individuals over time. Such data often exhibit {\em longitudinal correlation} (LC)…

Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have…

Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up…

Humans are capable of learning a new fine-grained concept with very little supervision, \emph{e.g.}, few exemplary images for a species of bird, yet our best deep learning systems need hundreds or thousands of labeled examples. In this…

The analysis of human microbiome data is often based on dimension-reduced graphical displays and clustering derived from vectors of microbial abundances in each sample. Common to these ordination methods is the use of biologically motivated…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…

Several works in implicit and explicit generative modeling empirically observed that feature-learning discriminators outperform fixed-kernel discriminators in terms of the sample quality of the models. We provide separation results between…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

The support vector machine algorithm with a quantum kernel estimator (QSVM-Kernel), as a leading example of a quantum machine learning technique, has undergone significant advancements. Nevertheless, its integration with classical data…

Kernel function plays a crucial role in machine learning algorithms such as classifiers. In this paper, we aim to improve the classification performance and reduce the reading out burden of quantum classifiers. We devise a universally…

A general, {\em rectangular} kernel matrix may be defined as $K_{ij} = \kappa(x_i,y_j)$ where $\kappa(x,y)$ is a kernel function and where $X=\{x_i\}_{i=1}^m$ and $Y=\{y_i\}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank…

Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…

In recent years, quantum machine learning has emerged as a promising intersection between quantum physics and artificial intelligence, particularly in domains requiring advanced pattern recognition such as healthcare. This study…

Unsupervised learning of high-dimensional data is challenging due to irrelevant or noisy features obscuring underlying structures. It's common that only a few features, called the influential features, meaningfully define the clusters.…

Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…