arXiv research

Study improves denoising score matching under relaxed manifold assumptions.

We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the glob…

New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allo…

Adam converges to stationary points under relaxed conditions.

Study relaxes identification assumptions for natural direct effects in non-randomized settings.

Paper relaxes independence assumption for non-centered data.

The study revisits portfolio diversification by relaxing assumptions for skewed, multi-regime, and leptokurtic asset returns.

Paper relaxes convexity assumptions in mean curvature flow results.

We propose a new topic modeling procedure that takes advantage of the fact that the Latent Dirichlet Allocation (LDA) log likelihood function is asymptotically equivalent to the logarithm of the volume of the topic simplex. This allows topic modeling to be reformulated as finding the probability simplex that minimizes …

Paper relaxes stability and generalization assumptions for SGD.

The paper shows that relaxing assumptions about causal graphs can lead to exponentially large equivalence classes.

Paper tackles offline RL with weak assumptions on both function classes and data coverage.

New method relaxes TV distance for two-sample testing without distributional assumptions.

This paper analyzes the convergence of Federated Average under relaxed assumptions.

A generalization of the Flow-box Theorem is given. The assumption of continuous differentiability of the vector field is relaxed to a local Lipschitz condition. The theorem holds in any Banach space.

Paper presents a randomized algorithm for SPCA with high probability approximation.

Paper revisits set membership estimation for linear systems with relaxed disturbance bounds.

AR algorithm simplifies backpropagation with improved scalability and biological plausibility.

We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries. The proof is based on a covering number argument. Since the spectral norm is dual to the tensor…

Paper studies Adam's convergence under relaxed assumptions, proving a rate of O(poly(log T)/sqrt(T)).

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the difference of convex (DC) programming, and enjoys both strong computational and statist…

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

The paper examines $L^2$-torsion in fibration cases relaxing standard conditions.

We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.

Domain adaptation addresses the common problem when the target distribution generating our test data drifts from the source (training) distribution. While absent assumptions, domain adaptation is impossible, strict conditions, e.g. covariate or label shift, enable principled algorithms. Recently-proposed domain-adversa…

Paper optimizes private ReLU regression with relaxed assumptions.

We study the problem of controlling linear time-invariant systems with known noisy dynamics and adversarially chosen quadratic losses. We present the first efficient online learning algorithms in this setting that guarantee $O(\sqrt{T})$ regret under mild assumptions, where $T$ is the time horizon. Our algorithms rely …

The leverage effect-- the correlation between an asset's return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stoc…

This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.

Geometric technique determines exactness of SDP robustness certificate.

This thesis relaxes assumptions for causal discovery, making methods applicable to more complex systems.

We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avo…

Paper simplifies balancing weights by relaxing outcome assumptions.

Double machine learning improves causal effect estimation by relaxing assumptions.

A new method for efficient causal structure learning at scale.

GPIRT uses Gaussian processes to estimate latent traits and IRFs from binary responses.

New framework relaxes independence assumption for graph-mixing dependencies.

Paper proposes estimators for sparse PCA with oracle property.

New method improves GP regression by relaxing variational assumption.

In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …

Paper relaxes faithfulness assumption for causal discovery using interventions.

We generalize stochastic smoothing for gradient estimation of non-differentiable functions.

The stochastic block model (SBM) is a popular tool for community detection in networks, but fitting it by maximum likelihood (MLE) involves a computationally infeasible optimization problem. We propose a new semidefinite programming (SDP) solution to the problem of fitting the SBM, derived as a relaxation of the MLE. W…

Study proves optimal controls for stochastic Volterra equations with singular kernels.

A new GP interpolation method for better predictive distributions in ranges of interest.

We consider the question whether a static potential on an asymptotically flat 3-manifold can have nonempty zero set which extends to the infinity. We prove that this does not occur if the metric is asymptotically Schwarzschild with nonzero mass. If the asymptotic assumption is relaxed to the usual assumption under whic…

Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptoti…