Empirical median performs well in estimating location with varying scales.
problem Estimating location with varying scales in data.
method Analysis of empirical median as an estimator.
result Matching upper and lower bounds on estimation error.
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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.
168,695 papers · 148 categories
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48 results for “empirical settings”
New algorithm optimizes unimodal bandits using empirical divergence.
problem Optimizing decisions in multi-armed bandit problems with unimodal distributions.
method Indexed Minimum Empirical Divergence (IMED) adapted for unimodal structure.
result IMED-UB algorithm optimally exploits unimodal structure.
Empirical Bayes rates via variational approximations and prior decomposition.
problem Nonparametric and high-dimensional inference convergence rates.
method Variational perspective and prior decomposition.
result Empirical Bayes posterior rates derived from variational Bayes.
Concentration bounds for the empirical angular measure with statistical learning applicationsmath.ST
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
problem Estimating the angular measure in high-dimensional data with different distributions.
method Established bounds for the maximal deviations of the empirical angular measure from the true measure, using rank transformation and analyzing the most extreme observations.
result The bounds provide performance guarantees for statistical learning procedures in extreme regions, such as binary classification and anomaly detection.
In this paper, we present a simple analysis of {\bf fast rates} with {\it high probability} of {\bf empirical minimization} for {\it stochastic composite optimization} over a finite-dimensional bounded convex set with exponential concave loss functions and an arbitrary convex regularization. To the best of our knowledg…
New algorithms identify Pareto optimal sets in multi-objective bandit problems.
problem Identifying Pareto optimal sets in multi-objective bandit problems.
method Empirical Gap Elimination (EGE) algorithms combining hardness estimation and elimination schemes.
result Two EGE algorithms have exponentially decaying error probabilities with budget.
LOO prediction method improves generalization guarantees for arbitrary datasets.
problem Understanding LOO error guarantees in fully transductive settings for arbitrary datasets.
method Median of Level-Set Aggregation (MLSA) for empirical-risk level sets.
result Multiplicative oracle inequality for LOO error with complexity scaling.
New method for efficient inference in large datasets.
problem Statistical inference in massive datasets.
method Combines divide-and-conquer method and empirical likelihood.
result Reduces computation burden and demonstrates effectiveness.
Meta-learning framework improves model performance on few-shot classification tasks.
problem Improving model performance on few-shot classification tasks.
method Empirical Bayes formulation with synthetic gradients for transductive meta-learning.
result Meta-learning framework outperforms previous state-of-the-art methods on benchmarks.
A neural network method estimates densities from characteristic functions.
problem Estimating fixed-horizon probability densities from empirical characteristic functions.
method Data-driven Fourier-mixture neural-network method trained in Fourier space.
result Competitive performance and clear gains on heavy-tailed targets.
New method for PU learning with instance-dependent propensity scores.
problem Learning from positive and unlabeled data with instance-dependent labeling.
method Empirical risk minimization of joint risk function, alternating optimization of posterior probability and propensity score.
result The method achieves comparable or better performance than state-of-the-art methods.
Improved multi-group learning with group-realizable concepts.
problem Enhancing multi-group learning efficiency.
method Empirical risk minimization over group-realizable concepts.
result Improved sample complexity in group-realizable settings.
New method uses SURE to denoise signals, outperforming NPMLE.
problem Learning to optimally denoise signals corrupted by Gaussian noise.
method Hyvärinen's score matching (SM) is shown equivalent to SURE minimization.
result SURE achieves nearly parametric rates of convergence in empirical Bayes settings.
We study compressing empirical measures in finite RKHSs using convex optimization.
problem Efficiently approximating empirical measures in high-dimensional spaces.
method Convex optimization and lower bounds on ball size.
result High probability lower bounds on ball size under various conditions.
The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.
problem Optimal algorithms for combinatorial and linear bandits with practical sample complexity.
method Empirical process theory, Gaussian-width, minimizing experimental design objective.
result Sample complexity matches lower bounds, especially for combinatorial classes.
Estimates conversion probabilities from click sequences with privacy constraints.
problem Training models in advertising with limited direct click-conversion links.
method Formalizes learning from attribution sets, constructs unbiased estimator, applies Empirical Risk Minimization.
result Empirical Risk Minimization achieves generalization guarantees and robustness against prior errors.
Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
Empirical Decision Theorystat.ME
Empirical model tackles decision problems without specifying states of the world.
problem Decision problems under uncertainty with inaccessible states of the world.
method Empirical approach using observed act--consequence pairs as model primitives.
result Optimality in empirical decision problems addressed using protocol-based empirical choice functions.
In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared …
We propose a distributed approach to train deep neural networks (DNNs), which has guaranteed convergence theoretically and great scalability empirically: close to 6 times faster on instance of ImageNet data set when run with 6 machines. The proposed scheme is close to optimally scalable in terms of number of machines, …
Cryptocurrencies show similarities to traditional markets but also have unique characteristics.
problem Understanding the investment potential and characteristics of cryptocurrencies.
method Organized stylized facts and analyzed through empirical asset pricing.
result Cryptocurrencies exhibit similarities to traditional markets but also have distinct characteristics.
Reweighting improves risk bounds in certain data regions.
problem Improving risk bounds in classification and heteroscedastic regression.
method Weighted empirical risk minimization with a data-dependent weight function.
result A weighted ERM estimator can achieve superior performance in specific sub-regions.
Paper shows ERM's suboptimality due to bias, not variance.
problem Understanding why ERM fails to achieve optimal rates.
method Probabilistic and admissibility proofs for ERM in various settings.
result ERM's suboptimality is due to bias, not variance.
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corres…
Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would li…
The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
Analyzes the complexity of linear hypothesis sets using Rademacher complexity.
problem Understanding the complexity of linear hypothesis sets for various norms.
method Tight analysis of empirical Rademacher complexity for linear hypothesis classes with bounded weights.
result Improved bounds on Rademacher complexity for linear hypothesis sets, matching or improving existing results.
The paper provides theoretical guarantees for optimized sampling in compressed sensing, showing error vanishes with more measurements.
problem Theoretical and practical improvements in compressed sensing with optimized sampling schemes.
method Theoretical analysis and empirical experiments with optimized sampling schemes for subsampled unitary matrices.
result The error caused by measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming Gaussian noise.
New algorithm closes empirical gap in PFSGD performance.
problem Empirical performance gap between tuned SGD and PFSGD.
method Parameter-free algorithm based on Coin-Betting ODE updates.
result New algorithm outperforms tuned baselines and matches optimal performance.
New method uses unlabeled data to improve generalization bounds for deep learning.
problem Vacuous guarantees and shrinking holdout sets for overparameterized models.
method Augmenting labeled training set with unlabeled data and training as usual.
result Proves tight upper bounds on true risk for 0-1 empirical risk minimization.
Improved Frank-Wolfe method reduces dependence on data size for empirical risk minimization.
problem Reducing dependence on number of data observations in Frank-Wolfe methods.
method Taylor-series approximated gradients applied to Frank-Wolfe method.
result Significant speed-ups over existing methods on real-world datasets.
ERM performs well in feature learning with minimal feature maps.
problem Empirical risk minimization in feature learning with square loss.
method Asymptotic and non-asymptotic analysis of ERM performance.
result Excess risk quantiles of ERM match those of oracle procedure under certain conditions.
VIB is Half Bayesstat.ML
VIB balances empirical and Bayesian approaches in predictive models.
problem Balancing empirical and Bayesian methods in predictive models.
method VIB as a compromise between empirical and Bayesian objectives.
result VIB minimizes risks due to finite sampling of targets.
Empirical study of IRMv1, an invariant risk minimization framework.
problem Learning predictors invariant to spurious correlations across different training environments.
method Extending ColoredMNIST experiment to various settings.
result IRMv1 performs better as spurious correlation varies more widely.
New insights into empirical Bayes and compound decision problems with improved regret bounds.
problem Estimating means of normally or Poisson distributed vectors under squared loss.
method Combines Bayesian and frequentist approaches using data-driven estimators.
result Optimal regret bounds for Poisson and normal mean models, resolving conjectures.
Motivated by the task of hyperparameter optimization, we introduce the non-stochastic best-arm identification problem. Within the multi-armed bandit literature, the cumulative regret objective enjoys algorithms and analyses for both the non-stochastic and stochastic settings while to the best of our knowledge, the best…
We present a first attempt to elucidate a theoretical and empirical approach to design the reward provided by a natural language environment to some structure learning agent. To this end, we revisit the Information Theory of unsupervised induction of phrase-structure grammars to characterize the behavior of simulated a…
We tackle the issue of classifier combinations when observations have multiple views. Our method jointly learns view-specific weighted majority vote classifiers (i.e. for each view) over a set of base voters, and a second weighted majority vote classifier over the set of these view-specific weighted majority vote class…
Develops statistical confidence sets for multidimensional scaling.
problem Statistical uncertainty in multidimensional scaling of noisy data.
method Formal statistical framework, distributional convergence results, uniform confidence sets, bootstrap procedures.
result Construction of reliable confidence sets for latent configurations in multidimensional scaling.
Improves model classification accuracy in black-box settings.
problem Difficulty in inferring model properties due to limited query access.
method Introduces discriminative factorization to distinguish high-quality queries.
result Probability of chance-level classification decreases exponentially with query budget.
Generalizes conformal prediction to multiple learnable parameters for efficient prediction sets.
problem Learning valid and efficient prediction sets with low-capacity function classes.
method Constrained empirical risk minimization (ERM) with gradient-based optimization of differentiable surrogate losses and Lagrangians.
result Achieves approximate valid population coverage and near-optimal efficiency within class.
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sa…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or …
Spectral features of the empirical moment matrix constitute a resourceful tool for unveiling properties of a cloud of points, among which, density, support and latent structures. It is already well known that the empirical moment matrix encodes a great deal of subtle attributes of the underlying measure. Starting from …
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the …
The paper tackles fair set-valued classification under demographic parity constraints.
problem Set-valued classification can amplify discriminatory bias, especially in multiclass settings.
method Proposes two strategies: an oracle-based method and a proxy method, both aiming to satisfy demographic parity and expected size constraints.
result Established distribution-free convergence rates and excess-risk bounds for both methods.
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets …