arXiv research

Kernel-based tests for shape constraints in finance.

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty in dealing with non-Euclidean geometry. In this paper, motivated by the extrins…

Adaptive RBF-KAN improves KANs by dynamically adjusting kernel parameters.

Paper tackles hard shape constraints in kernel machines.

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between …

This paper proposes the adaptation of Support Vector Data Description (SVDD) to the multiple kernel case (MK-SVDD), based on SimpleMKL. It also introduces a variant called Slim-MK-SVDD that is able to produce a tighter frontier around the data. For the sake of comparison, the equivalent methods are also developed for O…

2L-FUSE enhances feature sparsity through kernel learning.

We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance matrix of the process to the kernel matrix. The square root of the correlation f…

We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers…

New quantization methods improve accuracy of Random Fourier Features.

We develop a new route through which to explore $\kerΨ_X$, the kernel of the $π_1$-shape group homomorphism determined by a general space $X$, and establish, for each locally path connected, paracompact Hausdorff space $X$, $\kerΨ_X$ is precisely the Spanier group of $X$.

Unified understanding of neural representation similarity measures.

Researchers prove long-time existence for two landmark Brownian motion.

Unified framework for hard affine SDP constraints in vRKHSs.

DNAMite creates interpretable, calibrated survival analysis models.

Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposi…

The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.

Paper introduces a new kernel model for PSD-valued functions with theoretical guarantees and applications.

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an …

A new distributed clustering framework using distributional kernel.

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persist…

Proposes DILATE and STRIPE++ for precise time series forecasting.

LLMs learn probability density functions in-context, showing distinct learning trajectories.

The paper proposes a new method for modeling and quantifying uncertainty in multiple closed curves.

In this paper, we present experimental results obtained from retraining the last layer of the Inception v3 model in classifying images of human faces into one of five basic face shapes. The accuracy of the retrained Inception v3 model was compared with that of the following classification methods that uses facial landm…

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological summaries, most noticeably the Persistence Diagram, are typically defined in comple…

In this paper, we introduce a new image representation based on a multilayer kernel machine. Unlike traditional kernel methods where data representation is decoupled from the prediction task, we learn how to shape the kernel with supervision. We proceed by first proposing improvements of the recently-introduced convolu…

Estimation of facial expressions, as spatio-temporal processes, can take advantage of kernel methods if one considers facial landmark positions and their motion in 3D space. We applied support vector classification with kernels derived from dynamic time-warping similarity measures. We achieved over 99% accuracy - measu…

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape ove…

Deep vanilla transformers trained without shortcuts achieve similar performance to standard models.

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy topological properties. Nowadays, it is highly desired to develop a statistical framewo…

Proposes a new hyperprior and predictive criterion for weakly informative hyperprior in relevance vector machine.

New kernel models multi-output Gaussian processes accurately.

In-BO optimizes complex constrained domains using SIn-GP surrogate models.

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its practical applicability. We provide a scheme for learning a kernel parameterized by …

Most methods for time series classification that attain state-of-the-art accuracy have high computational complexity, requiring significant training time even for smaller datasets, and are intractable for larger datasets. Additionally, many existing methods focus on a single type of feature such as shape or frequency. …

In this paper, we address the problem of orientation that naturally arises when representing shapes like curves or surfaces as currents. In the field of computational anatomy, the framework of currents has indeed proved very efficient to model a wide variety of shapes. However, in such approaches, orientation of shapes…

Since their emergence in the 1990's, the support vector machine and the AdaBoost algorithm have spawned a wave of research in statistical machine learning. Much of this new research falls into one of two broad categories: kernel methods and ensemble methods. In this expository article, I discuss the main ideas behind t…

We propose a generic spatiotemporal event forecasting method, which we developed for the National Institute of Justice's (NIJ) Real-Time Crime Forecasting Challenge. Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian …

Over-parameterized CNNs show U-shaped test risk with depth increase.

The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.

Presents STRIPE model for probabilistic forecasting of non-stationary time series.

ResNets and their GP generalization align ideas via function space warping, revealing robust properties and connections to image registration.

We study the risk of minimum-norm interpolants of data in Reproducing Kernel Hilbert Spaces. Our upper bounds on the risk are of a multiple-descent shape for the various scalings of $d = n^α$, $α\in(0,1)$, for the input dimension $d$ and sample size $n$. Empirical evidence supports our finding that minimum-norm interpo…

Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a well-known tool to extract robust topological features, and outputs as \textit{persist…

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they are routinely used to describe topological properties of complicated shapes. PDs enjoy strong stability properties and have proven their utility in various learning contexts. They do not, however, live in a space naturally endo…

AEN-RBF kernel improves robustness in Bayesian optimization for complex systems.

We answer Mark Kac's famous question, "can one hear the shape of a drum?" in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the tra…