arXiv research

Study error bounds in evaluating distributional computational graphs.

Establishes statistical and computational bounds for influence diagnostics.

We study the fundamental tradeoffs between computational tractability and statistical accuracy for a general family of hypothesis testing problems with combinatorial structures. Based upon an oracle model of computation, which captures the interactions between algorithms and data, we establish a general lower bound tha…

Given a diagram D of a knot K, we give easily computable bounds for Rasmussen's concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for diagrams satisfying a given condition the bounds are tight. As a corollary we improve on previously known Bennequin-type bounds on the …

New computations show various properties of bounded cohomology in finitely presented groups.

A new method to measure neural network expressiveness using tighter upper bounds.

New method prunes large causal bounds LPs for scalable inference.

The study provides risk bounds for reservoir computing systems.

There has been renewed recent interest in developing effective lower bounds for Dynamic Time Warping (DTW) distance between time series. These have many applications in time series indexing, clustering, forecasting, regression and classification. One of the key time series classification algorithms, the nearest neighbo…

New method reduces computational cost for estimating PAC-Bayes bounds.

The paper proposes modern computational methods for optimizing reinsurance contracts.

Two new algorithms reduce online kernel regression's computational cost while maintaining optimal regret bounds.

New computational lower bounds for clustering and related problems.

New tighter confidence bounds for sequential kernel regression.

Computes bounds on mosaic number of Legendrian knots.

Computes upper bounds for instanton knot homology.

Study finds new knots that bound Möbius bands in 4D space.

Paper studies statistical-computational trade-offs in tensor PCA and related problems.

New bounds improve deep learning performance efficiently.

We accelerate min-max optimization and apply it to minimal bounding sphere problems.

Improved bounds for proximal gradient algorithms with computational errors.

We simplify evaluation of Ollivier-Ricci curvature bounds in hypergraphs.

Suppose $C$ is a compact, $n$-edged two-cell of the centered dual decomposition of a locally finite set in the hyperbolic plane, a coarsening of the Delaunay tessellation which was introduced in the author's prior work. We describe an effectively computable lower bound on the area of $C$, given an $n$-tuple of positive…

Paper improves neural network robustness analysis for safety-critical systems.

In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these algorithms perform in "typical" scenarios, or how far the best known theoretical…

Study on computable online learning with new conditions and complexities.

In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials $f$, $g \in \mathbb{Z}[x,y]$ and an arbitrary polynomial $h \in \mathbb{Z}[x,y]$, each of total degree less than $n$ and with integer coefficients of ab…

The paper improves bounds on the complexity of computing link polynomials.

Neural networks compute bounds on multi-asset derivatives.

New lower bounds for linear classification problems in high dimensions.

Quantum reservoirs risk bounds are analyzed using Rademacher complexity.

Computational limitations require more model parameters for robust learning.

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre (FKG) type inequalities, and are computed by m…

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression ove…

Method calculates systolic length of modular curves.

This paper extends financial theory to measure learnable market structure under computational constraints.

Lower bounds show linear complexity for linear regression.

We introduce a new class of links for which we give a lower bound for the slice genus $g_*$, using the generalized Rasmussen invariant. We show that this bound, in some cases, allows one to compute $g_*$ exactly; in particular, we compute $g_*$ for torus links. We also study another link invariant: the strong slice gen…

Computes bounds on reach and r-convexity from point cloud data.

Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model validation errors without actually training the model itself. A key idea behind ou…

New bounds found for ribbon numbers of knots and links.

Bounds on geodesic distances on Stiefel manifold derived from new metrics.

Sharp bounds for Kirby-Thompson invariants of knotted surfaces computed.

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of $[0,1]^2$, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bo…

We give a new lower bound for the first gap $λ_2 - λ_1$ of the Dirichlet eigenvalues of the Schr{ö}dinger operator on a bounded convex domain $Ω$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new bound is explicit and computable.

This paper develops efficient bounds on the Wasserstein metric for discrete measures.

This paper establishes for the first time the predictive performance of speed priors and their computational complexity. A speed prior is essentially a probability distribution that puts low probability on strings that are not efficiently computable. We propose a variant to the original speed prior (Schmidhuber, 2002),…

Improved Thompson Sampling algorithms for bandits with tighter regret bounds.