Related papers: High dimensional gaussian classification
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…
It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
We consider high-dimensional regression with a count response modeled by Poisson or negative binomial generalized linear model (GLM). We propose a penalized maximum likelihood estimator with a properly chosen complexity penalty and…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of…
Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
We introduce Bayesian hierarchical models for predicting high-dimensional tabular survey data which can be distributed from one or multiple classes of distributions (e.g., Gaussian, Poisson, Binomial, etc.). We adopt a Bayesian…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
We extend the standard Bayesian multivariate Gaussian generative data classifier by considering a generalization of the conjugate, normal-Wishart prior distribution and by deriving the hyperparameters analytically via evidence maximization.…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…