arXiv research

SIC detects elbows in error curves automatically.

A new criterion selects models in overparameterized settings.

New method improves matrix completion accuracy, especially in noisy data.

Spectral Independence Criterion helps infer cause-effect relationships in time series.

A criterion for training-free time-lagged spectral embeddings of multivariate time series

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be o…

Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral information is accompanied by the challenges like high dimensionality, singularity, lim…

Wave operators and spectral stability for Dirac operators under Ricci flow.

Spectral flow connects manifold geometry to rigidity criteria.

For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times \mathbb{R}^2$ satisfies the criterion. Our main tool is a spectral sequence that we der…

We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a topological model for the connected components of $X$. Both algorithms work by selectin…

Let $Γ$ be a relatively hyperbolic group and let $μ$ be an admissible symmetric finitely supported probability measure on $Γ$. We extend Floyd-Ancona type inequalities up to the spectral radius of $μ$. We then show that when the parabolic subgroups are virtually abelian, the Martin boundary of the induced random walk o…

With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspective. The majority of these works however focus on adapting the …

We introduce a new criterion to determine the order of an autoregressive model fitted to time series data. It has the benefits of the two well-known model selection techniques, the Akaike information criterion and the Bayesian information criterion. When the data is generated from a finite order autoregression, the Bay…

The study examines spectral properties of the Laplacian on forms for open Riemannian manifolds.

New criterion improves predictive evaluation in weighted inference scenarios.

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Non-standard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper present…

A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of…

New spectral Dehn function characterizes word-hyperbolic groups.

In this paper, we study an insurer's reinsurance-investment problem under a mean-variance criterion. We show that excess-loss is the unique equilibrium reinsurance strategy under a spectrally negative Lévy insurance model when the reinsurance premium is computed according to the expected value premium principle. Furthe…

The paper proves wave operator existence and completeness for Hodge Laplacians.

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

One of the longstanding open problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. We propose automated mode…

Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.

Complete criterion for VoI in multi-decision influence diagrams established.

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predicti…

Paper proposes a new flatness measure for neural networks to improve generalization.

LS improves model selection for singular statistical models.

SplitWise enhances stepwise regression by adaptively encoding numeric predictors into binary features.

In this paper, we propose an information-theoretic exploration strategy for stochastic, discrete multi-armed bandits that achieves optimal regret. Our strategy is based on the value of information criterion. This criterion measures the trade-off between policy information and obtainable rewards. High amounts of policy …

Optimal spectral method found for inhomogeneous spiked Wigner model.

Nontrivial boundary Dehn twist found on K3#K3 manifold.

A new criterion HBIC improves model selection for factor analysis with missing data.

When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both paradigms have their pros and cons. While minimum cut clusterings are sensitive t…

Statistical inference is considered for variables of interest, called primary variables, when auxiliary variables are observed along with the primary variables. We consider the setting of incomplete data analysis, where some primary variables are not observed. Utilizing a parametric model of joint distribution of prima…

Proposes a deep network for multi-class classification using spectral training and Gaussian kernel.

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…

This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Expe…

The paper derives an equation linking WAIC and WBIC for singular models.

We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a simple example of the application of this criterion and a demonstration of the natura…

Paper generalizes Bakry-Émery calculus for curvature and applies to Markov chains.

We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling. The information criteria are Akaike's information criterion (AIC), the…

Enhances graph neural networks with spectral and topological information.

Paper introduces a new metric to select optimal Graph Shift Operator for GNNs.

The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often reduce to the same optimization problem. However, the nonconvexity of the object…

When the in-sample Sharpe ratio is obtained by optimizing over a k-dimensional parameter space, it is a biased estimator for what can be expected on unseen data (out-of-sample). We derive (1) an unbiased estimator adjusting for both sources of bias: noise fit and estimation error. We then show (2) how to use the adjust…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…

We prove a completely new integral criterion for the existence and completeness of the wave operators $W_{\pm}(-Δ_h,-Δ_g, I_{g,h})$ corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators $-Δ_j$, $j=1,2$, that are induced by two quasi-isometric complete Riemannian metrics $g$ and $h$ o…