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.
This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression, spline smoothing or locally weighted regression, and the choice of a kernel in multiple kern…
A novel feature selection method using noise-based hypothesis testing improves feature selection accuracy.
problem Challenges in feature selection for complex, high-dimensional datasets.
method Introduces multiple random noise features and evaluates feature importance against noise feature maxima using non-parametric bootstrap-based hypothesis testing.
result Outperforms existing methods in simulated and real-world datasets.
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random…
This paper presents a tensor multiplication based smoothing algorithm that follows a two step denoising method. Unlike other traditional averaging approaches, our approach uses an element based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a l…
This paper improves parameter estimation for autonomous systems with unmodeled dynamics.
problem Accurate parameter estimation for risk-aware autonomous systems with unmodeled dynamics.
method Spectral lines-based approach for estimating parameters of dynamic models, allowing deterministic unmodeled dynamics.
result The proposed method leads to non-asymptotic bounds on parameter estimation error, robust to unmodeled dynamics, and matches existing literature in ideal conditions.
This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic topology used to extract topological information from data - in unsupervised learning …
We introduce a Noise-based prior Learning (NoL) approach for training neural networks that are intrinsically robust to adversarial attacks. We find that the implicit generative modeling of random noise with the same loss function used during posterior maximization, improves a model's understanding of the data manifold …
This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered a…
Attention mechanism is effective in both focusing the deep learning models on relevant features and interpreting them. However, attentions may be unreliable since the networks that generate them are often trained in a weakly-supervised manner. To overcome this limitation, we introduce the notion of input-dependent unce…
Recent advances in Capsule Networks (CapsNets) have shown their superior learning capability, compared to the traditional Convolutional Neural Networks (CNNs). However, the extremely high complexity of CapsNets limits their fast deployment in real-world applications. Moreover, while the resilience of CNNs have been ext…
Supervised training of deep learning models requires large labeled datasets. There is a growing interest in obtaining such datasets for medical image analysis applications. However, the impact of label noise has not received sufficient attention. Recent studies have shown that label noise can significantly impact the p…
Many unsupervised kernel methods rely on the estimation of the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). Both kernel CO and kernel CCO are sensitive to contaminated data, even when bounded positive definite kernels are used. To the best of our knowledge, there are few well…
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, …
Quantum kernels can be efficiently embedded into classical feature spaces.
problem Can all quantum kernels be efficiently embedded into classical feature spaces?
method Invoking computational universality and using techniques like random Fourier features, the authors show that certain classes of quantum kernels can be efficiently embedded.
result For shift-invariant and composition kernels, embedding quantum kernels are universal and efficient.
We present Random Partition Kernels, a new class of kernels derived by demonstrating a natural connection between random partitions of objects and kernels between those objects. We show how the construction can be used to create kernels from methods that would not normally be viewed as random partitions, such as Random…
In this paper, we compare 5 different nonlinear kernels: min-max, RBF, fRBF (folded RBF), acos, and acos-χ2, on a wide range of publicly available datasets. The proposed fRBF kernel performs very similarly to the RBF kernel. Both RBF and fRBF kernels require an important tuning parameter (γ). Interestingly, for a …
In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary kernels, and propose a family of spectral kernels that extends existing approac…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce a new algorithm for kernel learning that combines a {\em continuous set of base …