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.
Paper proposes a new method to learn distribution kernels via entropy maximization.
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features …
Optimal kernel in KR can be data-dependent, improving model performance.
A new MMD-based test combines kernels for two-sample testing without splitting data.
Estimates KRR risk from training data for various kernels and hyperparameters.
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size, a prohibitive cost in the large-data setting. Random feature maps (RFMs) and the…
Bayesian neural networks explore rare fluctuations for better feature learning.
Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expan…
Paper establishes a generalization bound for gradient flow using a data-dependent kernel.
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection phase is often ignored. In fact, in theoretical works most of the time assumptio…
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
IDK improves anomaly detection for points and groups without explicit learning.
New algorithm achieves data-dependent regret bounds in MDPs with unknown transitions.
Random features approach has been widely used for kernel approximation in large-scale machine learning. A number of recent studies have explored data-dependent sampling of features, modifying the stochastic oracle from which random features are sampled. While proposed techniques in this realm improve the approximation,…
Neural networks can learn kernel machines with a data-dependent kernel.
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of features required to achieve optimal learning bounds. Leverage scores introduce an op…
Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability of kernel methods is limited for large scale datasets. Random Fourier Features (R…
New decentralized KRR algorithm adapts to node-specific data.
New bounds for online portfolio selection without smoothness assumptions.
The strategy of early stopping is a regularization technique based on choosing a stopping time for an iterative algorithm. Focusing on non-parametric regression in a reproducing kernel Hilbert space, we analyze the early stopping strategy for a form of gradient-descent applied to the least-squares loss function. We pro…
Linearized attention fails to converge to NTK limit even at large widths.
The paper improves PAC-Bayes bounds for data-dependent predictors.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sam…
Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.
The study improves representation learning bounds using data-dependent Gaussian mixtures.
We present a data dependent generalization bound for a large class of regularized algorithms which implement structured sparsity constraints. The bound can be applied to standard squared-norm regularization, the Lasso, the group Lasso, some versions of the group Lasso with overlapping groups, multiple kernel learning a…
Proposes DP-MERF for privacy-preserving synthetic data generation.
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for…
A new data-adaptive prior stabilizes kernel learning in operators.
Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering, classification, feature selection, and data fusion. The standard CCA however, does not expl…
Learning can be seen as approximating an unknown function by interpolating the training data. Kriging offers a solution to this problem based on the prior specification of a kernel. We explore a numerical approximation approach to kernel selection/construction based on the simple premise that a kernel must be good if t…
PS-DME evaluates model performance and reliability after data-dependent selection.
New KD-tree based method for private synthetic data generation.
Paper introduces method to estimate animal motion on unknown submanifolds using Koopman operator.
Laplace kernel feature selection offers statistical guarantees for nonparametric models with few samples.
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good kernel has to be chosen. Picking a good kernel is a very challenging problem in its…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. …
The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning. The distribution from which the random features are drawn impacts the number of features required to efficiently perform a learning task. Recently, it has been shown that employing data-dependent …
Adaptive source selection for positive transfer in linear models improves target dataset performance.
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a generalization of standard PCA, for the setting where multiple datasets are availabl…
Develops methods to adjust prediction set coverage based on post-selection analysis.
Two-layer neural networks learn efficiently using kernel methods in mean-field analysis.
Two adaptive kernel selection methods improve the accuracy of Kernelized Diffusion Maps.
Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is generally not well documented in the literature. It is the goal of this paper to in…
Optimizes kernel discrepancies by selecting subsets efficiently.
Adaptive kernels from neural networks improve model performance.
Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementat…