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arXiv research

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.

168,657 papers · 148 categories

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184368552736 · Jun 202019922001200920172026
48 results for finite datasets

Analyzes symmetries in neural networks to predict learning dynamics.

problem Understanding the dynamics of neural network parameters during training.
method Unified theoretical framework based on symmetries and conservation laws.
result Symmetries impose geometric constraints on gradients and Hessians, leading to conservation laws.

Paper explores fair classification with bounded disparity using finite datasets.

problem Ensuring fairness in binary classification with protected groups.
method Minimax optimal approach with fairness constraints and demographic disparity control.
result Proposes FairBayes-DDP+ method that achieves minimax lower bound on fairness-aware excess risk.

Privacy concerns have led to the development of privacy-preserving approaches for learning models from sensitive data. Yet, in practice, even models learned with privacy guarantees can inadvertently memorize unique training examples or leak sensitive features. To identify such privacy violations, existing model auditin…

2019-11-08abs ↗pdf ↗

Split conformal prediction provides finite-sample guarantees for black-box models without distributional assumptions.

problem Weak performance guarantees for modern predictive models under minimal assumptions.
method Develops finite-sample guarantees for split conformal prediction, a method that uses nested prediction sets and order statistics.
result The coverage of prediction sets based on order statistics stochastically dominates the Beta distribution.

Paper improves generalization bounds for multi-kernel learning with mixed datasets.

problem Improving generalization for multi-kernel learning with mixed Markov chain datasets.
method Developed novel generalization bounds with O(logm)O(\sqrt{\log m}) and O(1/n)O(1/\sqrt{n}) dependencies.
result Added terms compensate for dependency among samples in mixed datasets.

The likelihood function of a finite mixture model is a non-convex function with multiple local maxima and commonly used iterative algorithms such as EM will converge to different solutions depending on initial conditions. In this paper we ask: is it possible to assess how far we are from the global maximum of the likel…

2016-08-18abs ↗pdf ↗

Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of h…

2014-07-16abs ↗pdf ↗

Transformers can interpolate finite input sequences exactly.

problem Interpolating finite input sequences of arbitrary lengths.
method Constructing a transformer with alternating feed-forward and self-attention layers, and low-rank parameter matrices.
result Exact interpolation of datasets of finite input sequences in R^d with corresponding output sequences of smaller or equal length.

Study shows offline RL with partial coverage and weak function classes is possible.

problem Learning optimal policies from logged data with function approximation.
method Marginalized Importance Sampling (MIS) with additional covering distribution.
result Finite-sample guarantees for sample-efficient offline RL for general MDPs.

Probabilistic SR method speeds up high-fidelity simulations with reliable uncertainty estimates.

problem Lack of reliable uncertainty quantification in deep-learning based SR methods.
method Statistical Finite Element Method and energy-based generative modeling.
result Efficient high-resolution predictions with inherent uncertainty estimates.

Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical D…

2015-12-05abs ↗pdf ↗

Exact inference method for Wasserstein distance with finite-sample coverage.

problem Asymptotic approximation methods for Wasserstein distance lack finite-sample validity.
method Selective Inference inspired approach for exact inference.
result Valid confidence interval for Wasserstein distance with finite-sample coverage.

The paper studies the graph geometry of finite groups, creating a dataset and analyzing its properties.

problem Understanding how group-theoretic structure is reflected in Cayley graph observables.
method Construction of a dataset of Cayley graphs for groups of order up to 767, analysis of graph statistics, and comparison of model performance.
result Graph statistics are highly informative for predicting group properties, and GNNs can recover substantial structural signal.

Proposes a method to ensure low losses across all subpopulations in large datasets.

problem Standard practice of minimizing average loss fails to guarantee low losses across all subpopulations in heterogeneous datasets.
method Convex procedure that controls worst-case performance over all subpopulations of a given size with finite-sample convergence guarantees.
result Empirically, the worst-case procedure learns models that do well against unseen subpopulations.

Empirical study compares wide neural networks to kernel methods, resolving open questions.

problem Understanding the relationship between wide neural networks and kernel methods.
method Large-scale empirical study using various neural network architectures and kernel methods.
result Wide neural networks outperform fully-connected finite-width networks in some cases, but underperform convolutional finite-width networks.

We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions b…

2019-09-05abs ↗pdf ↗

The paper analyzes Laplace learning for Gaussian measure data in infinite dimensions, proving convergence.

problem Analyzing Laplace learning for infinite-dimensional Gaussian measure data.
method Minimizes Dirichlet energy on a graph constructed from the full dataset.
result Proves pointwise convergence of the graph Dirichlet energy for Gaussian measure data.

An approximate method for conducting resampling in Lasso, the 1\ell_1 penalized linear regression, in a semi-analytic manner is developed, whereby the average over the resampled datasets is directly computed without repeated numerical sampling, thus enabling an inference free of the statistical fluctuations due to sam…

2018-02-28abs ↗pdf ↗

Empirical study shows standard CNNs deviate from NTK predictions.

problem Understanding how standard finite-width CNNs behave compared to their infinite-width NTK counterparts.
method Empirical analysis of AlexNet and LeNet architectures.
result Standard CNNs deviate significantly from their NTK counterparts, but deviation decreases with wider networks.

In many real-world applications, we want to exploit multiple source datasets of similar tasks to learn a model for a different but related target dataset -- e.g., recognizing characters of a new font using a set of different fonts. While most recent research has considered ad-hoc combination rules to address this probl…

2019-09-11abs ↗pdf ↗

The study reveals a transition in neural network performance from infinite-width to variance-limited behavior as dataset size increases.

problem Understanding the transition from infinite-width to variance-limited behavior in neural networks.
method Empirical study of the transition from infinite-width to variance-limited behavior as a function of sample size and network width.
result The critical sample size \( P^* \) is approximately \( \sqrt{N} \) for polynomial regression with ReLU networks.

Improved accuracy in dynamic response variation analysis using multi-fidelity data fusion.

problem Inefficient characterization of dynamic response variation due to limited high-fidelity data.
method Composite Neural Network fusion approach for multi-level, heterogeneous datasets.
result Improved accuracy in frequency response variation characterization.

Non-parametric estimators improve quickest changepoint detection under irregular sequence lengths.

problem Limited and irregular sequence lengths hinder application of ARL and ADD in QCD.
method Analogies with survival analysis to model detection probabilities under truncation.
result KM-ARL and KM-ADD non-parametric estimators are asymptotically unbiased.

The paper solves IRL for Bayesian stopping time problems.

problem Identifying optimal actions in Bayesian stopping time problems.
method Novel IRL framework using Bayesian revealed preferences.
result Identifies optimality and constructs cost function estimates.

Infinite-dimensional SBDMs improve image generation across multiple resolutions.

problem Efficient image generation at high resolutions and across different levels.
method Developed SBDMs in infinite-dimensional setting, using trace class operators and operator networks.
result Improved efficiency and generalization across resolution levels.