Related papers: A Distance Covariance-based Kernel for Nonlinear C…
Multiple datasets containing different types of features may be available for a given task. For instance, users' profiles can be used to group users for recommendation systems. In addition, a model can also use users' historical behaviors…
Distance metrics and their nonlinear variant play a crucial role in machine learning based real-world problem solving. We demonstrated how Euclidean and cosine distance measures differ not only theoretically but also in real-world medical…
In this study, a scalable online kernel learning framework is proposed for estimating bidirectional causal effects in systems characterized by mutual dependence and heteroskedasticity. Traditional causal inference often focuses on…
Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper,…
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
Competing risk data appear widely in modern biomedical research. Cause-specific hazard models are often used to deal with competing risk data in the past two decades. There is no current study on the kernel likelihood method for the…
Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…
We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived…
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical…
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Nonlinear machine-learning models are increasingly used to discover causal relationships in time-series data, yet the interpretation of their outputs remains poorly understood. In particular, causal scores produced by regularized neural…
We introduce a new approach to functional causal modeling from observational data, called Causal Generative Neural Networks (CGNN). CGNN leverages the power of neural networks to learn a generative model of the joint distribution of the…
By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…
Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…