A new method ReCPE removes the need for a distributional assumption in PU learning.
problem Training binary classifiers with only positive and unlabeled data without negative data.
method Regrouping CPE (ReCPE) that constructs an auxiliary distribution to ensure positive data support is never in negative data support.
result ReCPE improves all state-of-the-art CPE methods on various datasets, indicating the need for the distributional assumption.
Emputation learns imputation models guided by missingness assumptions.
problem Learning imputation models for missing data given observed data.
method Guided by specific missingness assumptions, Emputation trains a deep generative model to learn the extrapolation distribution of missing variables.
result The population minimizer of the emputation risk recovers the target extrapolation distribution under various identification assumptions.
New method relaxes TV distance for two-sample testing without distributional assumptions.
problem Challenges in certifying equality or providing tight bounds on TV distance for two distributions.
method Examined blurred total variation distance, a relaxation of TV distance.
result Provided theoretical guarantees for upper and lower bounds on blurred TV distance.
We study the problem of aggregation noisy labels. Usually, it is solved by proposing a stochastic model for the process of generating noisy labels and then estimating the model parameters using the observed noisy labels. A traditional assumption underlying previously introduced generative models is that each object has…
Bagging stabilizes models without distributional assumptions.
problem Stability of machine learning models without distributional assumptions.
method Derives a finite-sample guarantee on bagging stability for any model.
result Guarantee applies to many bagging variants and is optimal.
Existing generalization theories analyze the generalization performance mainly based on the model complexity and training process. The ignorance of the task properties, which results from the widely used IID assumption, makes these theories fail to interpret many generalization phenomena or guide practical learning tas…
The study reveals flaws in pruning criteria and proposes a new assumption for better filter selection.
problem Flaws in existing pruning criteria for CNNs.
method Empirical experiments and Convolutional Weight Distribution Assumption.
result The Convolutional Weight Distribution Assumption improves filter selection in pruning.
This thesis studies domain adaptation under minimal distribution similarity assumptions using moments.
problem Learning from samples with distributions different from training samples.
method Uses minimal similarity assumptions modeled by moments.
result Establishes learning bounds and algorithms for domain adaptation.
New polynomial convergence guarantees for SGM on general data distributions.
problem Efficient guarantees for multimodal and non-smooth distributions in SGM.
method Polynomial convergence guarantees for denoising diffusion models on general data distributions, with no assumptions on functional inequalities or smoothness.
result Wasserstein distance guarantees for distributions of bounded support or decaying tails, and TV guarantees for further smoothness assumptions.
This paper broadens contrastive learning for disentangled representations without strict data distribution assumptions.
problem Learning disentangled representations from data with specific assumptions.
method Extends theoretical guarantees for disentanglement to a broader family of contrastive methods, relaxing data distribution assumptions.
result Identifiability of true latents for four contrastive losses proved without common independence assumptions.
Improved k-NN active learning with local smoothness assumption.
problem Active learning convergence rates under smoothness assumptions.
method Designing an active learning algorithm with better convergence rate using local smoothness assumption for k-NN.
result Better convergence rate than in passive learning.
Paper shows robust generative learning with minimal assumptions on target distributions.
problem Learning generative models with minimal assumptions on target distributions.
method Lipschitz-regularized α-divergences with minimal assumptions. result Stable learning across various target distributions with minimal assumptions.
New algorithm for precise changepoint localization without assumptions.
problem Offline changepoint localization in arbitrary distributions.
method Distribution-free algorithm CONformal CHangepoint localization (CONCH) using exchangeability arguments.
result Derives principled score functions for informative and small confidence sets with normalized length shrinking to zero.
Hard to estimate L2-accurate scores without strong assumptions.
problem Estimating the score of unknown data distributions accurately.
method Reduction to generating samples and leveraging lattice-based cryptography hardness.
result Score estimation is computationally hard even with polynomial sample complexity.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O(d/n) in bounded distributions. Proposes a new stock prediction method that accounts for market dynamics.
problem The dynamic nature of the stock market invalidates traditional machine learning assumptions.
method Develops a second-order learning paradigm with multi-scale patterns.
result Demonstrates effectiveness in stock prediction on real-world data.
The ability to adequately model risks is crucial for insurance companies. The method of "Copula-based hierarchical risk aggregation" by Arbenz et al. offers a flexible way in doing so and has attracted much attention recently. We briefly introduce the aggregation tree model as well as the sampling algorithm proposed by…
CCN estimates full potential outcome distributions without restrictive assumptions.
problem Estimating CATE is insufficient; full potential outcome distributions provide greater insights.
method Collaborating Causal Networks (CCN) learns full potential outcome distributions without restrictive assumptions.
result CCN learns distributions that asymptotically capture true potential outcome distributions.
There is a large body of work on convergence rates either in passive or active learning. Here we outline some of the results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness and the margin noise. We also discuss the relative merits of these underlying assumpti…
We study the wealth distribution of the Bouchaud--Mézard (BM) model on complex networks. It has been known that this distribution depends on the topology of network by numerical simulations, however, no one have succeeded to explain it. Using "adiabatic" and "independent" assumptions along with the central-limit theore…
In the mixture models problem it is assumed that there are K distributions θ1,…,θK and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances with their generating distributions, or to identify the parameters of the hidden distribu…
Paper shows local SGD outperforms mini-batch SGD under certain conditions.
problem Proving local SGD's superiority in distributed learning with heterogeneous data.
method New lower and upper bounds for local SGD under first-order heterogeneity assumptions.
result Local SGD is min-max optimal under certain conditions, resolving understanding of distributed optimization.
Gradient methods learn a single neuron under mild assumptions.
problem Learning a single neuron with gradient methods under realistic conditions.
method Gradient methods applied to a single neuron model.
result Positive guarantees achieved under mild assumptions, beyond previous literature.
New method transfers causal mechanisms for few-shot domain adaptation.
problem Few labeled target domain data for regression problems.
method Mechanism transfer using structural equations in causal modeling.
result Method can adapt from apparently different distributions.
In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with standard results in the literature, which either make distributional assumption…
New findings show learning deeper neural networks is hard even with Gaussian inputs and non-degenerate weights.
problem The computational complexity of learning neural networks, especially deeper ones.
method Smoothed analysis framework and local pseudorandom generators.
result Learning depth-3 ReLU networks under Gaussian input distribution is hard even if weight matrices are non-degenerate.
Bounds on factual and counterfactual distributions under measurement error in discrete models.
problem Measurement errors in discrete data and their impact on inference.
method Expressing modeling assumptions as linear constraints and using linear programming to derive bounds.
result Sharp bounds on factual and counterfactual distributions for various models, including instrumental variable scenarios.
Proposes a deep model for Bayesian quantile regression without Gaussian assumptions.
problem Uncertainty quantification from single forward-pass models is computationally expensive and restrictive.
method Deep evidential learning for Bayesian quantile regression.
result Achieves calibrated uncertainties on non-Gaussian distributions.
Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distri…
As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear reg…
Study large deviations in life insurance portfolios without identical distributions.
problem Large deviations in life insurance portfolios with bounded losses and variances.
method Upper bound from standard large deviations, counterexample for full large deviation principle.
result Exponential bound for average loss exceeding a threshold.
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as f…
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as f…
Paper establishes fast convergence theory for diffusion models under minimal assumptions.
problem Establish theoretical guarantees for diffusion models under minimal assumptions.
method Developed a convergence theory for denoising diffusion probabilistic models (DDPM) under minimal assumptions.
result Achieved convergence rate of O(d/T) for target distributions with finite first-order moment.
Paper proves hardness of learning various complex models under local pseudorandom generators.
problem Hardness of learning various complex models.
method Existence of local pseudorandom generators.
result Proves hardness of learning shallow ReLU neural networks and other models.
Research tackles ML failure in non-similar data, introducing reliable algorithms.
problem Machine learning models fail in new data distributions.
method Formal definition, assumptions, and simple algorithms for reliable generalization.
result Introduction of algorithms providing more reliable generalization.
Conformal prediction offers distribution-free inference for complex models.
problem Traditional predictive inference methods are limited by assumptions about data distributions and model details.
method Conformal prediction uses symmetry assumptions and treats learning algorithms as black boxes.
result Conformal prediction provides exact finite-sample guarantees, even under limited assumptions.
In this paper we consider portmanteau tests for testing the adequacy of multiplicative seasonal autoregressive moving-average (SARMA) models under the assumption that the errors are uncorrelated but not necessarily independent.We relax the standard independence assumption on the error term in order to extend the range …
GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.
problem Learning invariant graph representations from different environments without additional assumptions.
method Developed GALA framework with minimal assumptions of variation sufficiency and consistency. Uses an assistant model to differentiate graph environment changes.
result Extracting maximally invariant subgraphs to proxy predictions identifies underlying invariant subgraphs for successful out-of-distribution generalization.
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presu…
New algorithm for safer machine learning with different testing and training distributions.
problem Challenges in modern machine learning where training and testing distributions differ.
method First-order optimization algorithm for superquantile-based learning.
result Promising numerical results show the approach's effectiveness.
New method calibrates probabilistic regression models without restrictive assumptions.
problem Ensuring predictive distributions accurately reflect true uncertainty.
method Nonparametric re-calibration algorithm based on conditional kernel mean embeddings.
result Consistently outperforms prior re-calibration approaches across various benchmarks.
Domain adaptation addresses the common problem when the target distribution generating our test data drifts from the source (training) distribution. While absent assumptions, domain adaptation is impossible, strict conditions, e.g. covariate or label shift, enable principled algorithms. Recently-proposed domain-adversa…
Hardness proof for agnostically learning halfspaces from worst-case lattice problems.
problem Agnostically learning halfspaces in the presence of noise.
method Reduction to worst-case lattice problems (GapSVP, SIVP).
result No efficient algorithm can achieve misclassification error better than 1/2 - γ under given hardness assumptions.
We use copulas to improve SLAM in uncertain environments.
problem Uncertain data association and nonlinear transition models in SLAM.
method Integrate copulas into a Sequential Monte Carlo estimator for SLAM.
result Our method effectively handles SLAM in uncertain environments.
For binary classification we establish learning rates up to the order of n−1 for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometr…
New method merges MCMC samples without distributional assumptions.
problem Efficiently merging MCMC samples from disjoint subsets.
method Diffusion generative modelling for density approximation.
result Outperforms existing methods on high-dimensional problems.
The study revisits portfolio diversification by relaxing assumptions for skewed, multi-regime, and leptokurtic asset returns.
problem Underestimation of risk in portfolio diversification due to assumptions that are inconsistent with real-world asset returns.
method Calibrated a Markov-modulated Levy process model to equity market data to demonstrate the merits of the approach.
result The calibrated models effectively match empirical moments and show the importance of relaxing assumptions in portfolio diversification.