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Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
Kernel method has been developed as one of the standard approaches for nonlinear learning, which however, does not scale to large data set due to its quadratic complexity in the number of samples. A number of kernel approximation methods…
A Greek weight associated to a parameterized random variable $Z(\lambda)$ is a random variable $\pi$ such that $\nabla_{\lambda}E[\phi(Z(\lambda))]=E[\phi(Z(\lambda))\pi]$ for any function $\phi$. The importance of the set of Greek weights…
Score-based explainable machine-learning techniques are often used to understand the logic behind black-box models. However, such explanation techniques are often computationally expensive, which limits their application in time-critical…
The Shapley value has become a popular method to attribute the prediction of a machine-learning model on an input to its base features. The use of the Shapley value is justified by citing [16] showing that it is the \emph{unique} method…
Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo…
Data valuation has found various applications in machine learning, such as data filtering, efficient learning and incentives for data sharing. The most popular current approach to data valuation is the Shapley value. While popular for its…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
Kernel methods provide a flexible and theoretically grounded approach to nonlinear and nonparametric learning. While memory and run-time requirements hinder their applicability to large datasets, many low-rank kernel approximations, such as…
Shapley values are model-agnostic methods for explaining model predictions. Many commonly used methods of computing Shapley values, known as off-manifold methods, rely on model evaluations on out-of-distribution input samples. Consequently,…
Kernel size selection in Convolutional Neural Networks (CNNs) is a critical but often overlooked design decision that affects receptive field, feature extraction, computational cost, and model accuracy. This paper proposes the Best Kernel…
Transformer-based semantic retrieval is highly effective, yet in many deployments the dominant cost lies in online query encoding rather than corpus indexing. We study the fixed-teacher query-adaptation problem and ask whether repeated…
The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient…
The proliferation of large models has intensified the need for efficient data valuation methods to quantify the contribution of individual data providers. Traditional approaches, such as game-theory-based Shapley value and…
Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a…
Kernel methods are widely used in causal inference for tasks such as treatment effect estimation, policy evaluation, and policy learning. The bootstrap is a standard tool for uncertainty quantification because of its broad applicability. As…
Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Due to their power and ease of use, tree-based machine learning models, such as random forests and gradient-boosted tree ensembles, have become very popular. To interpret them, local feature attributions based on marginal expectations, e.g.…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…