A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New algorithms find half-optimal independent sets in sparse graphs.
Size-independent neural transfer for RDDL planning.
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have improved dependence on the network depth, and under some additional assumptions, are…
Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test sca…
Proposes SVI for covariate-shift generalization with sparse variable independence.
We give a covering number bound for deep learning networks that is independent of the size of the network. The key for the simple analysis is that for linear classifiers, rotating the data doesn't affect the covering number. Thus, we can ignore the rotation part of each layer's linear transformation, and get the coveri…
In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classi…
In this paper we perform a statistical analysis over the returns and relative prices of the CAC and the S\&P with the purpose of analyzing the intra-day seasonalities of single and cross-sectional stock dynamics. In order to do that, we characterized the dynamics of a stock (or a set of stocks) by the evolut…
Deep nets learn structured densities without dimensionality issues.
Paper improves CMAB regret bounds by reducing batch-size dependency.
USP test improves on Pearson's chi-squared and -test for independence.
E-CIT framework reduces CITs' computational burden and improves causal discovery performance.
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …
A new algorithm for robust causal discovery in small sample sizes.
We consider large-scale studies in which it is of interest to test a very large number of hypotheses, and then to estimate the effect sizes corresponding to the rejected hypotheses. For instance, this setting arises in the analysis of gene expression or DNA sequencing data. However, naive estimates of the effect sizes …
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling i…
New test detects independence in streaming data, adapting to data complexity.
Improved sample complexity for ReLU networks with norm constraints.
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal dist…
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by con…
Novel bounds for SGLD show generalization error decreases with more samples.
The study finds a trade-off between model size, test loss, and training loss for linear predictors.
This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables are independent or not, a question that comes up in many fields like causality and neuroscience. While quantities like correlation o…
Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a p…
The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster centers from a sketch, i.e. from a drastically compressed representation of the traini…
New metrics for high-dimensional data improve on energy distance.
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …
New bounds on sample size for identifying mixture models with grouped samples.
This paper explores the problem of learning transforms for image compression via autoencoders. Usually, the rate-distortion performances of image compression are tuned by varying the quantization step size. In the case of autoen-coders, this in principle would require learning one transform per rate-distortion point at…
New method tests causal relationships from data without needing to learn the entire graph.
Proposes a differentiable hypergeometric distribution for learning group importance.
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are structurally similar to real networks. An important research problem is to identify the…
Improved batch-size independent regret bounds for nonlinear reward functions.
Recent works have cast some light on the mystery of why deep nets fit any data and generalize despite being very overparametrized. This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: (i) Using a tighter char…
We present a new similarity measure based on information theoretic measures which is superior than Normalized Compression Distance for clustering problems and inherits the useful properties of conditional Kolmogorov complexity. We show that Normalized Compression Dictionary Size and Normalized Compression Dictionary En…
New method generates private synthetic data without domain size dependence.
L2S unifies SARAH for sum of losses with improved convergence.
We add size factor to CAPM and normalize residuals by Volatility Index.
A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To address this issue, we further extend the correlation learning to marginal nonp…
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referr…
A new method reduces feature screening cost from to .
This work studies scaling laws for low-precision training in high-dimensional linear regression.
GaussDetect-LiNGAM eliminates Gaussianity tests for causal discovery.
Learnable multiclass hypothesis classes don't always have a sample compression scheme of fixed size.
The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points ac…