Related papers: Structure Learning in Inverse Ising Problems Using…

While deep learning has outperformed other methods for various tasks, theoretical frameworks that explain its reason have not been fully established. To address this issue, we investigate the excess risk of two-layer ReLU neural networks in…

LASSO regularization is a popular regression tool to enhance the prediction accuracy of statistical models by performing variable selection through the $\ell_1$ penalty, initially formulated for the linear model and its variants. In this…

We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…

We consider the linear model $\mathbf{y} = \mathbf{X} \mathbf{\beta}_\star + \mathbf{\epsilon}$ with $\mathbf{X}\in \mathbb{R}^{n\times p}$ in the overparameterized regime $p>n$. We estimate $\mathbf{\beta}_\star$ via generalized (weighted)…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization…

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine…

Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…

Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…

Deep neural networks are applied in more and more areas of everyday life. However, they still lack essential abilities, such as robustly dealing with spatially transformed input signals. Approaches to mitigate this severe robustness issue…

Extreme learning machine (ELM) is a network model that arbitrarily initializes the first hidden layer and can be computed speedily. In order to improve the classification performance of ELM, a $\ell_2$ and $\ell_{0.5}$ regularization ELM…

The Ising model was originally developed to model magnetisation of solids in statistical physics. As a network of binary variables with the probability of becoming 'active' depending only on direct neighbours, the Ising model appears…

This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only…

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the…

Interpolators -- estimators that achieve zero training error -- have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum $\ell_2$…

The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction…

In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are…

Deep-learning-based methods for different applications have been shown vulnerable to adversarial examples. These examples make deployment of such models in safety-critical tasks questionable. Use of deep neural networks as inverse problem…

In supervised learning, the regularization path is sometimes used as a convenient theoretical proxy for the optimization path of gradient descent initialized from zero. In this paper, we study a modification of the regularization path for…

In this paper, we study norm-based regularization methods for neural networks. We compare existing penalization approaches and introduce two regularization strategies that extend classical ridge- and lasso-type penalties to neural network…