PGF kernels analyze spherical data using generalized RBF kernels.
problem Analysis of spherical data.
method Introduced PGF kernels and a semi-parametric learning algorithm.
result PGF kernels generalize RBF kernels for spherical data.
On-device research index
arXiv research
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.
168,695 papers · 148 categories
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48 results for “general parametric kernels”
Efficiently models event-based data with general parametric kernels.
problem Inference for Hawkes processes with general parametric kernels requires large datasets.
method Developed a fast gradient-based solver using a discretized version of events.
result Improved estimation of pattern latency in brain signals.
Study provides guarantees for kernel clustering under non-parametric mixtures.
problem Statistical guarantees for kernel-based clustering without strong assumptions.
method Non-parametric mixture models, kernel-based clustering, consistency guarantees.
result Necessary and sufficient separability conditions for consistent clustering recovery.
This study examines when non-parametric methods are robust to adversarial examples.
problem Understanding when non-parametric methods are robust to adversarial examples.
method Examined general non-parametric methods and established conditions for r-consistency.
result Non-parametric methods like nearest neighbors and kernel classifiers are r-consistent when data is well-separated, while histograms are not.
Deep neural nets optimize kernel parameters for non-parametric two-sample tests.
problem Determining if two samples come from the same distribution.
method Deep kernels trained to maximize test power, adapting to distribution smoothness and shape.
result Deep kernels outperform simpler kernels in high dimensions and complex data.
Unified analysis for nonlinear parametric models in Bayesian optimization.
problem Limited theoretical guarantees for nonlinear parametric models in Bayesian optimization.
method Kernel-based framework for analyzing regularized nonlinear parametric models trained on adaptively collected data.
result Unified convergence guarantees for nonlinear acquisition and surrogate models.
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regre…
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
Develops a new method for learning non-parametric DAGs using RKHS.
problem Challenges of learning non-parametric causal models with large combinatorial search space.
method Uses reproducing kernel Hilbert spaces (RKHS) and sparsity-inducing regularization terms based on partial derivatives to enforce acyclicity.
result Shows improved performance through simulations and data analyses.
Sparse Gaussian processes with compact kernels for faster inference.
problem Efficient Gaussian process inference with high computational complexity.
method Parametric families of compactly-supported kernels for sparse matrix representations.
result Sub-quadratic inference complexity and improved performance on real-world tasks.
Develops flexible non-parametric ACFs using B-spline kernels.
problem Flexible modelling of the autocovariance function (ACF) in time-series, spatial, and spatio-temporal analysis.
method Derives the inverse Fourier transform of B-spline spectral bases to create a general class of non-parametric ACFs.
result Provides a provably dense, flexible, and general class of non-parametric ACFs for various types of processes.
We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this regularization strategy yields low-complexity sparse models where the number of eff…
This paper presents a semi-parametric algorithm for online learning of a robot inverse dynamics model. It combines the strength of the parametric and non-parametric modeling. The former exploits the rigid body dynamics equa- tion, while the latter exploits a suitable kernel function. We provide an extensive comparison …
Representation costs in data science: Unifying function-space views of parametric methods
problem Analyzing representation costs of parametric data-fitting methods
method Developing a general framework for analyzing representation costs through parameter-space regularizers
result Proving that many natural results hold in this abstract setting, including representer theorems for parametric methods on their native spaces
Paper proposes kernel-based tests for model misspecification.
problem Determining if a model is misspecified.
method Minimum distance estimators based on MMD and KSD.
result Correct test level maintained without data splitting.
Paper proposes a neural network for non-parametric Hawkes process kernel estimation.
problem Estimating non-parametric Hawkes process kernels efficiently and interpretably.
method Single hidden layer neural network for unbiased log-likelihood estimation of Hawkes processes.
result Proposed neural network achieves comparable or better performance than existing methods.
We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener-Hopf integral equations. A Wiener-Hopf argument allows one to prove that this system (in which the kernel matrix is the unknown) possesses a unique causal solution and consequentl…
Unified kernels for diverse applications in math and stats.
problem Unified kernels for diverse applications in math and stats.
method Unified parametric class of kernels, characterized by Sobolev spaces.
result Unified kernels encompass various known kernels and their properties.
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given samples, the time and space complexity of computing the KRR estimate scale as and respectively, and so is prohibitive in many cases. We prop…
Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on neural networks usually make restrictive parametric assumptions on the probabili…
Study optimizes estimating linear functionals from observational data without strict overlap.
problem Estimating linear functionals from observational data with strict overlap assumption violated.
method Kernel-based approach for non-asymptotic local minimax bounds.
result Achieves optimal risk for estimating linear functionals in observational data.
In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric model, namely Gaussian process modulated Hawkes process and propose an EM-variation…
Kernel Cox partially linear regression: building predictive models for cancer patients' survivalstat.ML
Paper develops a method to predict cancer patient survival using molecular profiles.
problem Accurately predicting cancer patient survival with complex survival-molecular profile relationships.
method Kernel Cox partially linear regression with a novel regularized garrotized kernel machine (RegGKM) method.
result The proposed method outperforms other methods in predicting survival accuracy.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework. Specifically, we learn local metrics optimized from parametric generative models. T…
New test assesses probabilistic model calibration without expensive approximations.
problem Assessing calibration of probabilistic models with scores.
method Kernel Calibration Conditional Stein Discrepancy (KCCSD) test using new score-based kernels.
result Control over type-I error with improved scalability and efficiency.
Faster convergence of kernel mean embeddings using variance information.
problem Speeding up the convergence rate of kernel mean embeddings.
method Leveraging variance information in reproducing kernel Hilbert space and estimating variance from data.
result Efficiently estimate variance information from data to achieve distribution-agnostic convergence bounds.
Error estimates for nonlinear PDEs using kernel/GP methods.
problem Error analysis of kernel/GP methods for nonlinear and parametric PDEs.
method Sobolev space error estimates based on minimizing norm property of the solution.
result Dimension-benign convergence rates for smooth solutions.
Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifoldsmath.DS
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based …
Improved outlier detection in hierarchical Gaussian Processes using Wasserstein-2 kernels.
problem Outlier detection limitations in stacked Gaussian Processes.
method Proposed a hybrid kernel combining Euclidean and Wasserstein-2 distances, emphasizing variance in Wasserstein-2 computations.
result Improved performance and enhanced out-of-distribution detection on various datasets.
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 generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of those in \cite{MinhGaussian2010}.
If pricing kernels are assumed non-negative then the inverse problem of finding the pricing kernel is well-posed. The constrained least squares method provides a consistent estimate of the pricing kernel. When the data are limited, a new method is suggested: relaxed maximization of the relative entropy. This estimator …
Paper introduces a new, tractable measure of model complexity.
problem Need for a reliable measure of model complexity.
method Mathematically rigorous measure based on gradient similarities.
result Generalizes to various model types and insights into double descent.
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a family of fast, flexible, lightly parametrized and general purpose kernel learning …
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive…
Detecting the emergence of abrupt property changes in time series is a challenging problem. Kernel two-sample test has been studied for this task which makes fewer assumptions on the distributions than traditional parametric approaches. However, selecting kernels is non-trivial in practice. Although kernel selection fo…
Gradient descent on MMD GAN parameter space converges globally to target distribution.
problem Convergence of gradient descent in Maximum Mean Discrepancy (MMD) GANs.
method Proposes a parametric kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN.
result Gradient descent on the generator's parameter space in gradient regularized MMD GAN is globally convergent to the target distribution under certain conditions.
Implicit Kernel Learningstat.ML
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While learning the kernel in a data driven way has been investigated, in this paper we e…
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These…
Kernel-based collocation methods for Heath-Jarrow-Morton models with Musiela parametrizationq-fin.CP
We propose kernel-based collocation methods for numerical solutions to Heath-Jarrow-Morton models with Musiela parametrization. The methods can be seen as the Euler-Maruyama approximation of some finite dimensional stochastic differential equations, and allow us to compute the derivative prices by the usual Monte Carlo…
We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the trans…
KQT-EWMA monitors multivariate data streams online with flexible and practical change detection.
problem Online monitoring of multivariate data streams for detecting changes.
method Combines Kernel-QuantTree histogram and EWMA statistic for non-parametric monitoring.
result Controls Average Run Length (ARL0) while achieving comparable detection delays.
Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task lea…
Geometric regularisation improves statistical models by avoiding degeneracy loci.
problem Non-identifiability, singular information, and moment indeterminacy in statistical models.
method Develops the geometric regularisation of distribution-kernel pairs using Whitney, Thom, and Mather theorems.
result Finite-dimensional weak transversality theorem for generic kernels, avoiding degeneracy strata of high codimension.
Gradient descent learns over-param neural nets better than NTK.
problem Learning over-parametrized neural networks with ReLU activations.
method Gradient descent from random initialization on a Gaussian input distribution.
result Gradient descent achieves population loss , while NTK achieves .
In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise scheme. Learning this data-adaptive matrix in a formulation-free strategy enlar…
Paper proves MS convergence for radially symmetric kernels with large bandwidths.
problem Proving convergence of mean shift algorithm with radially symmetric kernels.
method Analyzes convergence of mean shift algorithm with radially symmetric, positive definite kernels.
result Guaranteed convergence for sufficiently large bandwidth in any dimension.