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.
RTC-GTNLN model recovers traffic data from missing values and noise.
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this method is to generate the optimal projection matrix by considering both the sparsity as well as the corr…
We show that solutions of the Seiberg-Witten equations lead to non-trivial lower bounds for the L2-norm of the Weyl curvature of a compact Riemannian 4-manifold. These estimates are then used to derive new obstructions to the existence of Einstein metrics. These results considerably refine those previously obtained usi…
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile mini…
Improved sample efficiency in learning sparse Ising models.
A Riemannian metric on a compact 4-manifold is said to be Bach-flat if it is a critical point for the L2-norm of the Weyl curvature. When the Riemannian 4-manifold in question is a Kaehler surface, we provide a rough classification of solutions, followed by detailed results regarding each case in the classification. Th…
In this paper, we study the evolution of L2 p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L2 norm of a smooth p-form is non-increasing along the Ricci flow. The L^{\infty} norm is showe…
QAPCA uses quantum annealing for robust PCA.
We present an Automatic Relevance Determination prior Bayesian Neural Network(BNN-ARD) weight l2-norm measure as a feature importance statistic for the model-x knockoff filter. We show on both simulated data and the Norwegian wind farm dataset that the proposed feature importance statistic yields statistically signific…
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
Extends L2-norm LDA to 2D inputs using Bhattacharyya bound.
Support Vector Machine (SVM) is an efficient classification approach, which finds a hyperplane to separate data from different classes. This hyperplane is determined by support vectors. In existing SVM formulations, the objective function uses L2 norm or L1 norm on slack variables. The number of support vectors is a me…
We express characteristic numbers of compact hyperkähler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by ``wheels'' and we use the recently proved Wheeling Theorem to give a formula for the L2 …
We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproduci…
A new method reparameterizes ridge regression for faster, more interpretable results.
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on t…
Dynamic reinsurance aims to minimize surplus risk using martingale transport.
The purpose of this paper is to study the behaviour of sequences of generalised monopoles with a uniform bound on a certain L2-norm. We focus on the case that the target hyperKahler manifolds are Swann bundles. In 3-dimensional case, suppose that there exists an open submanifold Y' such that the hyperKahler potential a…
Forecast dam inflow using sea surface feature weights.
We derive new, sharp lower bounds for certain curvature functionals on the space of Riemannian metrics of a smooth compact 4-manifold with a non-trivial Seiberg-Witten invariant. These allow one, for example, to exactly compute the infimum of the L2-norm of Ricci curvature for all complex surfaces of general type. We a…
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of…
The support vector machine (SVM) is a widely used machine learning tool for classification based on statistical learning theory. Given a set of training data, the SVM finds a hyperplane that separates two different classes of data points by the largest distance. While the standard form of SVM uses L2-norm regularizatio…
We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate of our posterior update rule to the true probability function in…
Logit dynamics formula reveals self-regulation in softmax policy gradient methods.
Automl is the key technology for machine learning problem. Current state of art hyperparameter optimization methods are based on traditional black-box optimization methods like SMBO (SMAC, TPE). The objective function of black-box optimization is non-smooth, or time-consuming to evaluate, or in some way noisy. Recent y…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regulariz…
Humans are able to accelerate their learning by selecting training materials that are the most informative and at the appropriate level of difficulty. We propose a framework for distributing deep learning in which one set of workers search for the most informative examples in parallel while a single worker updates the …
So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined, i.e. when number of model parameters is much higher than the number of data point…
Robustness is an increasingly important property of machine learning models as they become more and more prevalent. We propose a defense against adversarial examples based on a k-nearest neighbor (kNN) on the intermediate activation of neural networks. Our scheme surpasses state-of-the-art defenses on MNIST and CIFAR-1…
This paper investigates the question of which smooth compact 4-manifolds admit Riemannian metrics that minimize the L2-norm of the curvature tensor. Metrics with this property are called OPTIMAL; Einstein metrics and scalar-flat anti-self-dual metrics provide us with two interesting classes of examples. Using twistor m…
Study evaluates various regularization methods for electricity price forecasting.
STRATA generates code adversarial examples efficiently without gradients.
Novel approach uses quasi-conformal geometry for OSA classification from cephalometry.
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discov…
Finding the diameter of a dataset in multidimensional Euclidean space is a well-established problem, with well-known algorithms. However, most of the algorithms found in the literature do not scale well with large values of data dimension, so the time complexity grows exponentially in most cases, which makes these algo…
The paper bounds the -norm of Euler class for foliations on 3-manifolds.
Adversarial perturbations fool deepfake detectors with high accuracy.
In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the value of a state under optimal subsequent decisions may be known to be convex or …
We consider the problem of sparse variable selection in nonparametric additive models, with the prior knowledge of the structure among the covariates to encourage those variables within a group to be selected jointly. Previous works either study the group sparsity in the parametric setting (e.g., group lasso), or addre…
In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values, but it cannot provide useful gradi…
Recently, deep neural network (DNN) has made a breakthrough in monaural source enhancement. Through a training step by using a large amount of data, DNN estimates a mapping between mixed signals and clean signals. At this time, we use an objective function that numerically expresses the quality of a mapping by DNN. In …
This paper proposes a method for machine learning from unlabeled data in the form of a time-series. The mapping that is learned is shown to extract slowly evolving information that would be useful for control applications, while efficiently filtering out unwanted, higher-frequency noise. The method consists of training…
We establish a uniform estimate for the injectivity radius of the past null cone of a point in a general Lorentzian manifold foliated by spacelike hypersurfaces and satisfying an upper curvature bound. Precisely, our main assumptions are, on one hand, upper bounds on the null curvature of the spacetime and the lapse fu…
Most of real-world graphs are dynamic, i.e., they change over time by a sequence of update operations. While the regression problem has been studied for static graphs and temporal graphs, it is not investigated for general dynamic graphs. In this paper, we study regression over dynamic graphs. First, we present the not…
Despite the great achievements of deep neural networks (DNNs), the vulnerability of state-of-the-art DNNs raises security concerns of DNNs in many application domains requiring high reliability.We propose the fault sneaking attack on DNNs, where the adversary aims to misclassify certain input images into any target lab…
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically …
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the weight normalization (WN) method [Salimans and Kingma, 2016] and a variant call…