arXiv research

We formulate statistical watermarking as hypothesis testing and establish near-optimal bounds.

Study examines Fed's pandemic communication strategies.

BL learns interpretable optimization structures from data.

Method for factor analysis in short panels without assuming sphericity or Gaussianity.

Hotelling's $T^2$-test for the mean of a multivariate normal distribution is one of the triumphs of classical multivariate analysis. It is uniformly most powerful among invariant tests, and admissible, proper Bayes, and locally and asymptotically minimax among all tests. Nonetheless, investigators often prefer non-inva…

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…

We show the existence of uniformly bounded sequences of increasing numbers of orthonormal sections of powers $L^k$ of a positive holomorphic line bundle $L$ on a compact Kähler manifold $M$. In particular, we construct for each positive integer $k$, orthonormal sections $s^k_1,\dots,s^k_{n_k}$ in $H^0(M,L^k)$, $n_k\geβ…

A new classifier improves one-class predictions on unevenly sampled data.

The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from $\mathbb{R}^n$ continue to hold with no additional restrictions. For a general Banach spaces we will see that the classical Reifenberg theorem holds, and that a we…

Uniformly finite Cannon--Thurston fibers in most hyperbolic settings.

Study on anisotropic curvature flow for noncompact convex hypersurfaces.

We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $α>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the ini…

Study of cable links of uniformly thick knots, revealing new isotopy phenomena.

It is well-known that quasi-isometries between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity …

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…

For any closed Riemannian three-manifold, we prove that for any sequence of closed embedded minimal surfaces with uniformly bounded index, the genus can only grow at most linearly with respect to the area.

The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly, and a power law when the saving factor is set diversely. The power distribution c…

Improved reasoning model by sampling from power distribution without additional training.

Uniformly random permutations converge to regular representation on surface groups.

Extends PPI to sequential setting, improving inference over time.

The study finds a limit on the volume growth of certain 3-manifolds.

Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation. Generalization with high probability has been established in a landmark paper of Bousque…

Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models…

Study of Fubini-Study forms on surfaces with punctures.

Study on positive scalar curvature and its impact on Ricci limit spaces.

We prove that on a punctured oriented surface with Euler characteristic chi < 0, the maximal cardinality of a set of essential simple arcs that are pairwise non-homotopic and intersecting at most once is 2|chi|(|chi|+1). This gives a cubic estimate in |chi| for a set of curves pairwise intersecting at most once on a cl…

We consider smooth solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, connected, four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that T is finite. In this case, we show that the metric space (M,d(t)) associated to (M,g(t)) converges uniformly in the C^0 s…

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the …

We show that the asymptotic dimension of a hyperbolic relatively hyperbolic graph is finite provided that this holds true uniformly for the peripheral subgraphs and for the electrifiation. We use this to show that the asymptotic dimension of the disk graph of a handlebody of genus at least two is at most quadratic in t…

We show that codimension one dimensional Jacobian of the barycentric straightening map is uniformly bounded for most of the higher rank symmetric spaces. As a consequence, we prove that the locally finite simplicial volume of most $\mathbb Q$-rank $1$ locally symmetric spaces is positive, which has been open for many y…

Symbolic dynamics for flows in high dimensions, extending previous work.

Established in the 30's, Schauder {\it a priori} estimates are among the most classical and powerful tools in the analysis of problems ruled by 2nd order elliptic PDEs. Since then, a central problem in regularity theory has been to understand Schauder type estimates fashioning particular borderline scenarios. In such c…

We find bounds for Weil-Petersson holomorphic sectional curvature, and the Weil-Petersson curvature operator in several regimes, that do not depend on the topology of the underlying surface. Among other results, we show that the minimal (most negative) eigenvalue of the curvature operator at any point in the Teichmülle…

We study the convergence of the Kähler-Ricci flow on a Fano manifold under some stability conditions. More precisely we assume that the first eingenvalue of the $\bar\partial$-operator acting on vector fields is uniformly bounded along the flow, and in addition the Mabuchi energy decays at most logarithmically. We then…

Major internet companies routinely perform tens of thousands of A/B tests each year. Such large-scale sequential experimentation has resulted in a recent spurt of new algorithms that can provably control the false discovery rate (FDR) in a fully online fashion. However, current state-of-the-art adaptive algorithms can …

The standard method of generating random weights and biases in feedforward neural networks with random hidden nodes, selects them both from the uniform distribution over the same fixed interval. In this work, we show the drawbacks of this approach and propose a new method of generating random parameters. This method en…

A new algorithm reduces communication in distributed SVD by $p$ factors.

In the problem of optimal investment with utility function defined on $(0,\infty)$, we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p…

Uniformly branching trees are equivalent to certain metric spaces.

Uniformly finite homology is a coarse homology theory, defined via chains that satisfy a uniform boundedness condition. By construction, uniformly finite homology carries a canonical $\ell^\infty$-semi-norm. We show that, for uniformly discrete spaces of bounded geometry, this semi-norm on uniformly finite homology in …

We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the correct feature space under certain generalized assumptions.We present four cas…

This paper concerns the evolution of complete noncompact locally uniformly convex hypersurface in Euclidean space by curvature flow, for which the normal speed $Φ$ is given by a power $β\geq 1$ of a monotone symmetric and homogeneous of degree one function $F$ of the principal curvatures. Under the assumption that $F$ …

We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold of dimension at most seven, can degenerate. Loosely speaking, our results show …

Robust tests control type I error under data corruption.

We propose Additive Powers-of-Two~(APoT) quantization, an efficient non-uniform quantization scheme for the bell-shaped and long-tailed distribution of weights and activations in neural networks. By constraining all quantization levels as the sum of Powers-of-Two terms, APoT quantization enjoys high computational effic…

Researchers create spectral triples for twisted crossed products using Kasparov's external product.

Proposes a framework for OOD detection combining multiple statistics.

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study many fundamental learning algorithms (e.g., $k$-nearest neighbors [Rogers and Wag…