Related papers: Refining quasi-probability kernels
We investigate the problem of algorithmic fairness in the case where sensitive and non-sensitive features are available and one aims to generate new, `oblivious', features that closely approximate the non-sensitive features, and are only…
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift…
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…
There is an intense and partly recent literature focussing on the problem of selecting the bandwidth parameter for kernel density estimators. Available methods are largely `very nonparametric', in the sense of not requiring any knowledge…
The quasi likelihood analysis is generalized to the partial quasi likelihood analysis. Limit theorems for the quasi likelihood estimators, especially the quasi Bayesian estimator, are derived in the situation where existence of a slow…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
Measuring similarity between incomplete data is a fundamental challenge in web mining, recommendation systems, and user behavior analysis. Traditional approaches either discard incomplete data or perform imputation as a preprocessing step,…
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…
The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…
Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel…
Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…
We address the problem of non-parametric multiple model comparison: given $l$ candidate models, decide whether each candidate is as good as the best one(s) or worse than it. We propose two statistical tests, each controlling a different…
In this paper we show if R is a filtered ring then we can define a quasi valuation. And if R is some kind of filtered ring then we can define a valuation. Then we prove some properties and relations for R.
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free…
As new advancements in the field of quantum computing lead to the development of increasingly complex programs, approaches to validate and debug these programs are becoming more important. To this end, methods employed in classical…