A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Develops interpretable low-dimensional kernels with conic discriminant functions.
Generative Kernel PCA explores latent spaces for data interpretation and novelty detection.
This paper makes kernels interpretable for wide feature matrices.
A method for interpreting SVMs using polynomial kernels, revealing model complexity.
FCM efficiently approximates committor function with interpretable kernel model.
The paper explores the identifiability and interpretability of Gaussian process models using different kernel structures.
Kernel methods' derivatives make complex models more interpretable.
A novel GP architecture, Thin and Deep GP, learns lower-dimensional representations without losing interpretability.
Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While there has been extensive research on the applications and properties of kernels, …
RFFNet scales kernel methods to large datasets by learning kernel relevance.
Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over composition functions. We propose interpretable DGP based on approximating DGP …
Proposes DR-ME test for interpretable distributional treatment effects.
Deep learning predicts drug prescriptions across global health records.
Prototype-based methods are of the particular interest for domain specialists and practitioners as they summarize a dataset by a small set of representatives. Therefore, in a classification setting, interpretability of the prototypes is as significant as the prediction accuracy of the algorithm. Nevertheless, the state…
Tree ensembles like RF and GBT can be seen as kernels, improving regression and classification performance.
TIME network simplifies complex physical processes with interpretable models.
In recent years, machine learning researchers have focused on methods to construct flexible and interpretable prediction models. However, an interpretability evaluation, a relationship between generalization performance and an interpretability of the model and a method for improving the interpretability have to be cons…
Deep networks are mathematically equivalent to kernel machines learned by gradient descent.
New approach interprets Nyström for kernel machines with geometric insight.
Sparse Kernel Flows learns dynamical systems from data.
Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first map the data into a high dimensional feature space using kernels prior to a projec…
Survival kernets scale deep kernel survival analysis to large datasets with interpretability and theoretical guarantees.
Bayesian TNKMs automatically infer model complexity and feature relevance.
Bayesian optimisation with graph kernels improves neural architecture search and provides interpretability.
Alzheimer's disease is a major cause of dementia. Its diagnosis requires accurate biomarkers that are sensitive to disease stages. In this respect, we regard probabilistic classification as a method of designing a probabilistic biomarker for disease staging. Probabilistic biomarkers naturally support the interpretation…
We investigate iterated compositions of weighted sums of Gaussian kernels and provide an interpretation of the construction that shows some similarities with the architectures of deep neural networks. On the theoretical side, we show that these kernels are universal and that SVMs using these kernels are universally con…
This paper introduces the concept of kernels on fuzzy sets as a similarity measure for -valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the intersection, the non-singleton and the distance-based kernels on fuzzy sets. Applicabili…
New interpretation of attention in Transformers and Graph Attention Networks.
We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coefficient of the small time asymptotic expansion of the heat kernel on the diagonal, and we interpret it in terms of curvature-like invariants o…
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…
Bayesian neural networks with Mercer priors for interpretable uncertainty quantification.
RKHS-SHAP uses Shapley values for kernel methods to provide feature attributions.
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite difficult, the use of a single kernel type may not be appropriate in all areas of the in…
Random Forest kernels improve performance in various regression and survival tasks.
Kernel methods linked to feature subspaces and maximal correlation kernels.
We introduce the convolutional spectral kernel (CSK), a novel family of non-stationary, nonparametric covariance kernels for Gaussian process (GP) models, derived from the convolution between two imaginary radial basis functions. We present a principled framework to interpret CSK, as well as other deep probabilistic mo…
There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for …
Improved Gaussian process models for interpretable predictions.
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…
Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirro…
RFAD uses random features to speed up dataset distillation.
Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor performance. We propose a novel model family of zero-inflated Gaussian processes (ZiGP) …
Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be useful to develop a new approach to some old classical problems as well as to obtain several new results, mostly related to hyperbolic geom…
Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.
A new method calculates intrinsic effective sample size for manifold-valued data.
A fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connecti…
KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.