Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
This work explains the structural origins of attention sinks in LLMs.
problem Initial tokens disproportionately monopolize attention scores in LLMs.
method Traced to self-attention's value aggregation process and FFN layer activations.
result Attention sinks form due to variance discrepancy and dimension disparity.
Unified method for MMD variance estimation improves accuracy and computational efficiency.
problem Variance estimation for MMD in nonparametric testing.
method Unified finite-sample characterization of MMD variance through U-statistic and Hoeffding decomposition; exact acceleration method for univariate case.
result Unified estimators improve accuracy and computational efficiency for MMD variance.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) d…
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
Proposes ENVAR for causal discovery in structural VAR models with equal noise variance.
problem Challenges in causal discovery from multivariate time series with contemporaneous effects.
method Introduces observational equivalence and the observational alignment discrepancy for structural VAR models with equal noise variance.
result Shows that multiple structural VAR parameterizations can induce the same stationary observed process law.
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl…
Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which usually causes subsampling bias, inflates generalization errors and jeopardizes the r…
New method uses generative models to estimate aleatoric uncertainty without strict data restrictions.
problem Estimating aleatoric uncertainty with limited data distribution or dimensionality.
method Conditional generative models and two metrics for measuring distributional discrepancies.
result Metrics accurately measure conditional distributional discrepancies and train competitive models.
Estimates and tests treatment effects on entire outcome distributions.
problem Treatment effects on entire outcome distributions, not just averages.
method Proposes a novel estimand and doubly robust estimator, develops a test.
result First test with provably valid type 1 error guarantees in this setting.
The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able to efficiently estimate the variance of this estimator is very helpful to vario…
Study on geodesics on random hyperbolic surfaces, showing variance asymptotic to X log X.
problem Distribution of closed geodesics on random hyperbolic surfaces.
method Viewing surfaces as random points in moduli space, studying weighted counting function.
result Variance in large genus limit is asymptotic to X log X, with exceptions.
New method for adaptive estimation and inference in econometric models without knowing smoothness.
problem Adaptive estimation and inference in ill-posed linear inverse problems with unknown smoothness.
method Discrepancy principle-based framework for adaptive hyperparameter selection.
result Achieves optimal rates in weak and strong metrics for linear functionals.
Derives token price process for AMM tokens, finds leverage effect and pricing discrepancies.
problem Derives token price process for AMM tokens.
method Derives CEV process for token price, derives closed-form option prices, introduces liquidity-adjusted Greeks.
result Token price process is CEV, with leverage effect and pricing discrepancies.
Kernelized cumulants improve statistical analysis in high-dimensional spaces.
problem Statistical analysis in high-dimensional spaces with low variance estimators.
method Extending cumulants to RKHS using tensor algebra and kernel trick.
result Kernelized cumulants provide new all-purpose statistics with computational tractability.
Study improves forecast accuracy of daily volatility to enhance portfolio performance.
problem Improving predictability of realized variance from market views.
method High-dimensional machine learning models and low-dimensional factor models used to forecast firm-level volatility.
result Marginal improvements in forecast error lead to significant gains in portfolio performance.
New method for MMD with unequal sample sizes improves test power.
problem Existing MMD methods assume equal sample sizes, discarding valuable data.
method Extended generalized U-statistics to handle unequal sample sizes.
result New asymptotic distributions and power optimization for MMD with unequal sample sizes.
Unified framework for clustering with auxiliary data.
problem Clustering with datasets reflecting similar but different latent structures.
method Adaptive Transfer Clustering (ATC) algorithm that optimizes bias-variance decomposition.
result ATC proves optimal under Gaussian mixture model and shows transfer benefits.
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness …
Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes imperative to distribute the implementation of such variance reduced methods. In this p…
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…
New method prunes classification trees for biased data.
problem Pruning classification trees in imbalanced training data.
method Optimal pruning procedure for inhomogeneous data.
result First efficient procedure for optimal pruning under covariate shift.
New discrepancy function compares discrete probability measures considering space geometry.
problem Comparing discrete probability measures in a geometrically meaningful way.
method Proposes the Fourier Discrepancy Function, proving convexity, differentiability, and providing gradient formula.
result Proves the Fourier Discrepancy is convex, twice differentiable, and provides an explicit gradient formula.
This paper introduces localized discrepancy theories for unsupervised domain adaptation.
problem Improving generalization bounds for unsupervised domain adaptation.
method Localized discrepancies defined on the hypothesis space after localization, leading to smaller and asymmetric values.
result Improved generalization bounds and sample complexity reduction.
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
The maximum mean discrepancy (MMD) is a recently proposed test statistic for two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this study we propose an efficient method called FastMMD. The core idea of FastMMD is …
Proposes a method to select variables for kernel two-sample tests.
problem Determining whether two samples have the same distribution using informative variables.
method A framework based on kernel maximum mean discrepancy (MMD) for selecting a subset of variables.
result The sample size requirements for the three kernels depend on the number of selected variables, not the data dimension.
MPMC generates low-discrepancy points using graph neural networks.
problem Generating efficient low-discrepancy point sets.
method Leveraging Graph Neural Networks to model geometric properties.
result Achieves state-of-the-art performance in generating low-discrepancy points.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
New biclustering algorithm in Hilbert spaces for complex data.
problem Discovering new biological functions in gene expression data.
method Model-free biclustering algorithm using energy distance and maximum mean discrepancy.
result The method can learn more general and complex cluster shapes.
Variance-Calibrated Modulation (VCM) addresses the likelihood trap in LLMs by reshaping the probability distribution before truncation.
problem LLMs fall into the likelihood trap, leading to repetitive degeneration and vocabulary dullness.
method VCM reshapes the probability distribution before truncation through Contextual Searchlight and Adaptive Self-Debiasing.
result VCM mitigates the likelihood trap across open-ended generation, factual QA, and mathematical reasoning.
This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy …
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
This paper refines MMD for domain adaptation by balancing intra-class and inter-class distances.
problem Balancing intra-class and inter-class distances for better feature discriminability in domain adaptation.
method The paper theoretically proves two facts about MMD and proposes a novel discriminative MMD method to balance intra-class and inter-class distances.
result The proposed method improves feature discriminability and outperforms state-of-the-art methods.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
The performance of standard learning procedures has been observed to differ widely across groups. Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). In this work, we point to a more subtle source of loss discrepancy---feature noise. Our mai…
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
The paper highlights the importance of model discrepancy in cardiac simulations.
problem Uncertainty in model structure and equations affects predictions.
method The authors use Gaussian processes and autoregressive-moving-average models to account for model discrepancy.
result Different methods to account for model discrepancy have advantages and shortcomings.
A new metric DJP-MMD improves domain adaptation by balancing transferability and discriminability.
problem Improving domain adaptation performance by balancing transferability and discriminability.
method Discriminative Joint Probability Maximum Mean Discrepancy (DJP-MMD) replaces the traditional joint MMD.
result DJP-MMD outperforms traditional MMDs in image classification tasks.
A new method for density estimation using mixture discrepancy and moments.
problem Generalizing histogram statistics to higher dimensions.
method Density estimation via mixture discrepancy and moments (DSP-mix and MSP).
result DSP-mix and MSP are computationally tractable and maintain accuracy with increased speed.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Bayes-consistent disagreement discrepancy loss improves model robustness.
problem Distribution shift in real-world neural network deployment.
method Introducing a novel disagreement loss that is Bayes consistent.
result Proves existing surrogates for disagreement discrepancy are not Bayes consistent.
Kernel semi-implicit variational inference improves variational inference without additional optimization.
problem Intractability of hierarchical semi-implicit distributions in variational inference.
method Kernel semi-implicit variational inference (KSIVI) using kernel methods to eliminate lower-level optimization.
result KSIVI reduces variational inference to kernel Stein discrepancy (KSD) optimization, improving expressiveness and tractability.
New method estimates model discrepancy without sampling for unnormalized models.
problem Evaluating and training unnormalized density models efficiently.
method Estimate Stein discrepancy using neural network parameterized vector function.
result Method outperforms existing goodness-of-fit tests and training methods.