Study distortion risk measures for step-weighted distributions.
problem Analyzing risk measures for specific distribution types.
method Investigate distortion risk measures of step-weighted distributions.
result Developed methods for calculating risk measures.
We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when row and column indexes are not selected independently), present a corrected var…
Survey on importance weighting in machine learning applications.
problem Distribution shift in supervised learning.
method Weighting objective function or probability distribution based on instance importance.
result Importance weighting can guarantee desirable statistical properties in distribution shift scenarios.
Generative models learn from biased data using weighted importance.
problem Learning from biased or related data distributions.
method Importance weighting to estimate loss with respect to target distribution.
result Effective in various settings with theoretical guarantees and good performance.
Theory of learning with weight-distribution constraints.
problem Understanding how structure influences function in neural networks.
method Statistical mechanical theory and optimal transport.
result Reduction in capacity due to constrained weight-distribution is related to Wasserstein distance.
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
New insights into neural network kernels for rectified MLPs.
problem Understanding the behavior of weight distributions in rectified MLPs.
method Deriving equivalent kernels for MLPs with ReLU or Leaky ReLU activations under various weight distributions.
result Kernels corresponding to layers with certain weight distributions are asymptotically universal and well approximated by Gaussian kernels.
Gradient descent with random weights in linear regression analyzed for various noise types.
problem Analyzing the impact of random noise on gradient descent in linear regression.
method Gradient descent with randomly weighted data points, various weighting distributions, geometric moment contraction.
result Characterization of implicit regularization and non-asymptotic convergence bounds.
A new method aligns source and target distributions by tuning their weights.
problem Domain adaptation on unlabeled target datasets using labeled source datasets.
method Weighted Joint Distribution Optimal Transport (WJDOT) method that finds alignment between source and target distributions and re-weighting of source distributions.
result Achieves state-of-the-art performance on simulated and real-life datasets.
Hardness proven for neural networks with natural weights.
problem Difficulty in learning neural networks with weights from natural distributions.
method Proved hardness for depth-2 networks with natural weights distributions.
result Most networks are hard to learn with natural weights.
The importance-weighted risk estimator can be skewed, leading to suboptimal regularization parameters.
problem Skewed sampling distribution of the importance-weighted risk estimator affects model selection.
method Empirical study of the sampling distribution of the importance-weighted risk estimator.
result The importance-weighted risk estimator produces overestimates for the majority of cases and underestimates for tail cases, leading to suboptimal regularization parameters.
The paper classifies vertices in weighted networks using spectral embedding and edge weight distributions.
problem Classifying vertices in weighted networks where edge weights and adjacencies encode class membership.
method Introduced a edge weight distribution matrix to the K-Block Stochastic Block Model for weighted networks. Developed classification procedures based on spectral embedding of the unweighted adjacency matrix under two assumptions on edge weight distributions.
result Proposed classifiers outperform quadratic discriminant analysis on transformed weighted networks.
Recently theoretical guarantees have been obtained for matrix completion in the non-uniform sampling regime. In particular, if the sampling distribution aligns with the underlying matrix's leverage scores, then with high probability nuclear norm minimization will exactly recover the low rank matrix. In this article, we…
A new model for detecting overlapping communities in weighted networks.
problem Community detection in overlapping weighted networks with mixed membership and edge weights.
method Mixed membership distribution-free (MMDF) model with an efficient spectral algorithm and fuzzy weighted modularity.
result The MMDF model can estimate community memberships and evaluate community quality for weighted networks.
Corrects distribution shift in target shift scenarios using importance weighting.
problem Analyzes importance weighting for correcting distribution shift under target shift.
method Analyzed importance-weighted kernel ridge regression under target shift.
result Shows that importance weighting corrects the train-test mismatch without altering input-space complexity.
Sharp analysis of out-of-distribution error in overparameterized models with importance weights.
problem Understanding and quantifying the degradation of performance in overparameterized models when faced with underrepresented data.
method Sharp analysis of an overparameterized Gaussian mixture model with spurious features and cost-sensitive interpolating solutions incorporating importance weights.
result Characterization of a novel tradeoff between worst-case robustness and average accuracy as a function of importance weight magnitude.
Optimal weights improve particle-based approximations of discrete distributions.
problem Improving particle-based approximations of discrete distributions.
method Proving optimality of weights and showing how to compute them efficiently.
result Optimal weights can be computed from existing particle-based methods without extra costs.
Adaptive sampling method improves efficiency in complex target distributions.
problem Efficiency of importance sampling in complex target distributions, especially multimodal distributions in high-dimensional spaces.
method Proposes an adaptive scheme combining global sampling with delayed weighting to promote efficient exploration of target distributions.
result The proposed algorithm is geometrically convergent under mild assumptions and demonstrates improved efficiency in various numerical experiments.
Extend CPS to non-exchangeable settings with observation-specific permutation weights
problem Calibrated predictive bands under distributional shifts
method Encoding distributional shifts through observation-specific permutation weights
result Shift-aware predictive systems remain valid
Paper characterizes sampling distributions of optimal portfolio weights and characteristics.
problem Characterizing sampling distributions of optimal portfolio weights and characteristics.
method Derives exact sampling distribution by stochastic representation.
result High-dimensional asymptotic distribution of optimal portfolio weights is multivariate normal.
Algorithm approximates target distribution using weight queries.
problem Approximating a distribution without sampling.
method Interactive algorithm using weight queries and UCB approach.
result Approximation bound on total variation distance.
Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.
problem Adapting empirical distributions to predefined constraints on moments, tail behavior, etc.
method Nonparametric distributional constraints, maximum entropy principle, optimal transport.
result Maximum entropy weight adjusted empirical distribution close to a specified distribution in optimal transport metric.
Distributed learning for related tasks using graph weights.
problem Learning multiple tasks on different machines.
method Weighted averaging of messages with skewing or stepsize control.
result Different tasks can be learned on different machines.
This paper examines weight initialization for 1-Lipschitz networks to improve robustness against adversarial attacks.
problem Improving the robustness of deep neural networks against adversarial attacks.
method Examined weight parametrization of AOL and SLL networks, calculated weight variance bounds, and demonstrated weight decay.
result Weight initialization causes deep 1-Lipschitz networks to decay to zero, and weight variance does not affect output variance distribution.
The paper proves a distribution claim for neural network Jacobians.
problem Distribution of singular values in deep neural networks.
method Free probability and random matrix theory techniques.
result Singular value distribution matches for specific cases.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
Proposes deep weight prior for improving neural network performance.
problem Improving neural network performance with limited training data.
method Defines deep weight prior (DWP) as an implicit distribution and proposes variational inference methods.
result Improves performance of Bayesian neural networks with limited data and accelerates conventional CNN training.
Proposes tracking DNN weights for uncertainty estimation.
problem Discarded information during DNN training.
method Tracks weights' trajectory during optimization.
result Competitive uncertainty estimation results.
WBCP improves conformal prediction for distribution shifts using weighted Dirichlet posteriors.
problem Handling distribution shifts in conformal prediction.
method Generalizes Bayesian Quadrature Conformal Prediction (BQ-CP) to arbitrary importance-weighted settings.
result WBCP maintains coverage guarantees while providing richer uncertainty information.
The paper analyzes prediction error in nonstationary settings using weighted risk minimization.
problem Prediction under distribution drift and nonstationary conditions.
method General decomposition of excess risk into learning and drift terms, proving oracle inequalities under mixing conditions.
result Oracle inequalities for the learning error, providing bounds that hold uniformly over arbitrary weight classes.
Proves equivalence of two types of Ricci curvature bounds.
problem Equivalence of distributional and synthetic Ricci curvature bounds.
method Analyzes weighted Riemannian manifolds with specific smoothness conditions.
result Proves equivalence of Ricci curvature bounds under given conditions.
Heuristic weighting improves denoising score matching without requiring noise distribution assumptions.
problem Improving denoising score matching without assuming noise distribution.
method Demonstrated heteroskedasticity, derived optimal weighting functions, and provided theoretical and empirical comparisons.
result Heuristical weighting function can achieve lower variance than optimal weighting, facilitating more stable and efficient training.
A distributed Nesterov method for arbitrary graphs achieves faster convergence.
problem Optimizing distributed systems over arbitrary graphs.
method Distributed Nesterov method ABN and its variation FROZEN. result Achieves acceleration compared to state-of-the-art methods.
Bayesian neural networks learn weights with closed-form updates.
problem Efficiently learning Bayesian neural networks with closed-form updates.
method Closed-form Bayesian inference for online learning of Gaussian-weighted BNNs.
result Closed-form expressions for sequential/online training of BNNs.
A new method for deep learning under distribution shift by iteratively refining importance weighting.
problem Handling distribution shift in deep learning models when training and test data distributions differ.
method Dynamic Importance Weighting (dynamic IW) that iterates between weight estimation and weighted classification, using a pre-trained feature extractor and stochastic optimization.
result Dynamic IW outperforms state-of-the-art methods in experiments with various types of distribution shift on multiple datasets.
A new method estimates treatment effects without strong assumptions.
problem Treatment effect estimation with strong model assumptions.
method Distribution learning-based weighting method.
result Our method outperforms existing methods in estimating ATT.
New method improves causal effect estimation by addressing imbalance in training data.
problem Imbalance between treatment and control groups in training data.
method Combines distributionally robust optimization and weight regularization.
result Consistent improvements over existing methods in experiments.
Improves prediction stability with model misspecification and distribution shift.
problem Inaccurate parameter estimation and instability of prediction in real-world applications.
method Proposes Decorrelated Weighting Regression (DWR) algorithm to optimize weights for samples and variables.
result Significantly improves accuracy of parameter estimation and prediction stability.
New loss function restores importance weighting in overparameterized models.
problem Restoring importance weighting in overparameterized neural networks.
method Introduced polynomially-tailed losses to restore effects of importance weighting.
result Polynomially-tailed losses improve performance in correcting distribution shift.
New method for initializing RBM weights without datasets.
problem No dataset-free weight-initialization for RBMs.
method Statistical mechanical analysis to derive Gaussian distribution with optimized standard deviation.
result Optimal weight initialization improves learning efficiency in RBMs.
Estimates causal effects using neural networks for balancing covariates.
problem Estimating causal effects from observational data.
method Neural Balancing Weights (NBW) using α-divergence for density ratio estimation. result Generalized approach for balancing multidimensional data.
Current-mode memristor crossbars enable neuromemristive systems with similar accuracy but different weight distributions.
problem Implementing weight matrices in neuromemristive systems via current-mode memristor crossbars.
method Derived theoretical results for weight range and distribution, developed a modified gradient descent rule for current-mode design, and performed behavioral simulations.
result Current-mode and voltage-mode designs achieve similar accuracy but use different feature representations.
CWAN tackles multi-source heterogeneous domain adaptation with conditional weighting.
problem Learning cross-domain samples from multiple heterogeneous domains.
method CWAN uses a feature transformer, label classifier, and domain discriminator to learn from multiple sources.
result CWAN outperforms state-of-the-art methods on four real-world datasets.
Diffusion models accurately recover mixture weights from generated samples despite score function insensitivity.
problem Score-based generative models often fail to learn correct relative mode amplitudes (mixture weights) from generated samples.
method Relate diffusion score matching (DSM) loss to mixture weight estimation error, define diffusion score sensitivity index (DSSI), and prove its governing role in mixture weight recovery.
result Generated samples can accurately recover mixture weights from the DSM loss, even when the target score is insensitive to mixture weights.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.
problem Underestimation of Value-at-Risk by traditional models in asset pricing.
method Developed an econometric framework combining heavy-tailed Student's t distributions with behavioral probability weighting. result Student's t specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points. The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…
New model for detecting communities in weighted bipartite networks.
problem No model for community detection in overlapping bipartite weighted networks.
method Introduces BiMMDF model allowing any distribution with block structure.
result Efficient algorithm with theoretical guarantee of consistent estimation.