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Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared…
Information retrieval (IR) systems traditionally aim to maximize metrics built on rankings, such as precision or NDCG. However, the non-differentiability of the ranking operation prevents direct optimization of such metrics in…
The estimation of probability density functions is a fundamental problem in science and engineering. However, common methods such as kernel density estimation (KDE) have been demonstrated to lack robustness, while more complex methods have…
In this paper, estimates are proven for convolution kernels associated to multipliers from a reasonably general class of compactly supported two-dimensional functions constructed out of real-analytic functions. These estimates are both for…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM…
Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using…
The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. This paper proposes a spherical Monte Carlo method with both theoretical analysis and numerical simulation. First,…
In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is…
In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…
We discuss suitable classes of diffusion processes, for which functionals relevant to finance can be computed via Monte Carlo methods. In particular, we construct exact simulation schemes for processes from this class. However, should the…
We propose an estimation method that we call functional average variance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of density and regression. Consistency results…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
In this note we provide a simple approximation theory motivation for the circular kernel density estimation and further explore the usefulness of the wrapped Cauchy kernel in this context. It is seen that the wrapped Cauchy kernel appears…
Multivariate conformal prediction requires nonconformity scores that compress residual vectors into scalars while preserving certain implicit geometric structure of the residual distribution. We introduce a Multivariate Kernel Score (MKS)…
A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…
We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
A density function for an algebraic invariant is a measurable function on $\mathbb{R}$ which measures the invariant on an $\mathbb{R}$-scale. This function carries a lot more information related to the invariant without seeking extra data.…