相关论文: Structure Learning in Inverse Ising Problems Using…

We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of…

We propose an adjusted 2SLS estimator for social network models when reported binary network links are misclassified (some zeros reported as ones and vice versa) due, e.g., to survey respondents' recall errors, or lapses in data input. We…

The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing…

Many statistical problems can be reduced to a linear inverse problem in which only a noisy version of the operator is available. Particular examples include random design regression, deconvolution problem, instrumental variable regression,…

We theoretically analyze the typical learning performance of $\ell_{1}$-regularized linear regression ($\ell_1$-LinR) for Ising model selection using the replica method from statistical mechanics. For typical random regular graphs in the…

Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…

In many modern applications of deep learning the neural network has many more parameters than the data points used for its training. Motivated by those practices, a large body of recent theoretical research has been devoted to studying…

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…

We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks. We derive a closed-form expression for the expected generalization…

Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…

Model collapse occurs when generative models degrade after repeatedly training on their own synthetic outputs. We study this effect in overparameterized linear regression in a setting where each iteration mixes fresh real labels with…

The identification of the network effect is based on either group size variation, the structure of the network or the relative position in the network. I provide easy-to-verify necessary conditions for identification of undirected network…

In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…

In Imitation Learning (IL), utilizing suboptimal and heterogeneous demonstrations presents a substantial challenge due to the varied nature of real-world data. However, standard IL algorithms consider these datasets as homogeneous, thereby…

We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we derive closed form expressions for the asymptotic bias,…

We construct custom regularization functions for use in supervised training of deep neural networks. Our technique is applicable when the ground-truth labels themselves exhibit internal structure; we derive a regularizer by learning an…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…