arXiv research

Complexity measures for neural nets with general activations using path-based norms.

This paper improves tail dependence analysis by introducing a path-based approach.

PathBoost boosts graph-level predictions using path-based features.

StrokeCoder uses Transformers to generate images from single examples.

Improved RL for knowledge graph reasoning with entity types.

Collective classification has been intensively studied due to its impact in many important applications, such as web mining, bioinformatics and citation analysis. Collective classification approaches exploit the dependencies of a group of linked objects whose class labels are correlated and need to be predicted simulta…

Proposes Geodesic Integrated Gradients (GIG) for more accurate feature attributions in deep networks.

Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based clustering (GOPC) algorithm in this paper. The GOPC algorithm is based on two facts: (1) …

A model predicts influential nodes in complex networks by considering indirect interactions.

The paper proposes a method to improve random forest classification accuracy by weighting trees based on their decision path reliability.

Adapts IG for better feature attributions and robustness.

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice mod…

Paper uncovers causal structures in Hawkes processes with latent subprocesses.

We consider the problem of clustering with the longest-leg path distance (LLPD) metric, which is informative for elongated and irregularly shaped clusters. We prove finite-sample guarantees on the performance of clustering with respect to this metric when random samples are drawn from multiple intrinsically low-dimensi…

Derives functional Itô formula for non-anticipative maps of rough paths.

We discuss a concept denoted as Conformal Prediction (CP) in this paper. While initially stemming from the world of machine learning, it was never applied or analyzed in the context of short-term electricity price forecasting. Therefore, we elaborate the aspects that render Conformal Prediction worthwhile to know and e…

CDA framework infers channel influence from aggregated data without user identifiers.

Study measures impact of data and neural net similarity on transferability in restaurant sales data.

To address the sparsity and cold start problem of collaborative filtering, researchers usually make use of side information, such as social networks or item attributes, to improve recommendation performance. This paper considers the knowledge graph as the source of side information. To address the limitations of existi…

Paper proposes a method to evaluate SME credit risk using meta paths.

Abstract compares two norms in holomorphic quadratic differentials.

GAGA accelerates 3D molecular generation by replacing long trajectories with Gaussian approximations.

We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this…

We introduce twisted Alexander norms of a compact connected orientable 3-manifold with first Betti number bigger than one generalizing norms of McMullen and Turaev. We show that twisted Alexander norms give lower bounds on the Thurston norm of a 3-manifold. Using these we completely determine the Thurston norm of many …

We study a regularizer which is defined as a parameterized infimum of quadratics, and which we call the box-norm. We show that the k-support norm, a regularizer proposed by [Argyriou et al, 2012] for sparse vector prediction problems, belongs to this family, and the box-norm can be generated as a perturbation of the fo…

This research develops a new model for cyber risk and insurance pricing.

KrigHedge uses Gaussian processes to approximate option Greeks efficiently.

New L0 norm added to TDA for market analysis.

The $k$-support norm is a regularizer which has been successfully applied to sparse vector prediction problems. We show that it belongs to a general class of norms which can be formulated as a parameterized infimum over quadratics. We further extend the $k$-support norm to matrices, and we observe that it is a special …

CNN layers with large norms are still robust to adversarial attacks.

Study on minimal hypersurfaces in a special normed space.

The paper defines minimal norm tensors for curvature and divergence tensors, explaining Weyl and Cotten tensors.

A result of Bangert states that the stable norm associated to any Riemannian metric on the $2$-torus $T^2$ is strictly convex. We demonstrate that the space of stable norms associated to metrics on $T^2$ forms a proper dense subset of the space of strictly convex norms on $\R^2$. In particular, given a strictly convex …

The spectral $k$-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank $k$ matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral $(k,p)$-support norm, whose additional para…

The Schatten quasi-norm can be used to bridge the gap between the nuclear norm and rank function, and is the tighter approximation to matrix rank. However, most existing Schatten quasi-norm minimization (SQNM) algorithms, as well as for nuclear norm minimization, are too slow or even impractical for large-scale problem…

Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations. Nuclear norm regularization is the prevailing convexifying technique for dealing …

We provide recovery guarantees for compressible signals that have been corrupted with noise and extend the framework introduced in \cite{bafna2018thwarting} to defend neural networks against $\ell_0$-norm, $\ell_2$-norm, and $\ell_{\infty}$-norm attacks. Our results are general as they can be applied to most unitary tr…

The study connects norms and filtrations on section rings of projective manifolds.

Future robots should follow human social norms in order to be useful and accepted in human society. In this paper, we leverage already existing social knowledge in human societies by capturing it in our framework through the notion of social norms. We show how norms can be used to guide a reinforcement learning agent t…

Functorial semi-norms on singular homology give refined "size" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm.

The paper proves inequalities linking geometric norms and Thurston norms in hyperbolic 3-manifolds.

Article provides polytopes as dual unit balls of Thurston norms on 3-manifolds.

Paper introduces new risk norms based on ES with flexible distortion functions.

We propose a set of convex low rank inducing norms for a coupled matrices and tensors (hereafter coupled tensors), which shares information between matrices and tensors through common modes. More specifically, we propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, w…

Over the past half-decade, many methods have been considered for neural architecture search (NAS). Bayesian optimization (BO), which has long had success in hyperparameter optimization, has recently emerged as a very promising strategy for NAS when it is coupled with a neural predictor. Recent work has proposed differe…

General $(α, β)$ norms are an important class of Minkowski norms which contains the original $(α, β)$ norms. In this note, by studying the behavior of the Darboux curves of the indicatrix, we give a characterization of 3-dimensional general $(α, β)$ norms. By studying the isoperimetric properties of the indicatrix, as …

Uniform convergence of interpolators proven for Gaussian data.

A new PCA method using T$\ell_1$-norm outperforms existing methods.