Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear regression where the model parameters, i.e., the unknowns, are distributed over the network. We adopt a statistical learning approach. In contrast to works that focus on the performance on the training data, we focus on the generalization error, i.e., the performance on unseen data. We provide high-probability bounds on the generalization error for both isotropic and correlated Gaussian data as well as sub-gaussian data. These results reveal the dependence of the generalization performance on the partitioning of the model over the network. In particular, our results show that the generalization error of the distributed solution can be substantially higher than that of the centralized solution even when the error on the training data is at the same level for both the centralized and distributed approaches. Our numerical results illustrate the performance with both real-world image data as well as synthetic data.

For a d-ary Boolean function Φ: {0, 1}d → {0, 1} and an assignment to its variables x = (x1, x2, . . . , xd) we consider the problem of finding those subsets of the variables that are sufficient to determine the function value with a given probability δ. This is motivated by the task of interpreting predictions of binary classifiers described as Boolean circuits, which can be seen as special cases of neural networks. We show that the problem of deciding whether such subsets of relevant variables of limited size k ≤ d exist is complete for the complexity class NPPP and thus, generally, unfeasible to solve. We then introduce a variant, in which it suffices to check whether a subset determines the function value with probability at least δ or at most δ − γ for 0 < γ < δ. This promise of a probability gap reduces the complexity to the class NPBPP. Finally, we show that finding the minimal set of relevant variables cannot be reasonably approximated, i.e. with an approximation factor d1−α for α > 0, by a polynomial time algorithm unless P = NP. This holds even with the promise of a probability gap.

Decision-making often requires accurate estimation of treatment effects from observational data. This is challenging as outcomes of alternative decisions are not observed and have to be estimated. Previous methods estimate outcomes based on unconfoundedness but neglect any constraints that unconfoundedness imposes on the outcomes. In this paper, we propose a novel regularization framework for estimating average treatment effects that exploits unconfoundedness. To this end, we formalize unconfoundedness as an orthogonality constraint, which ensures that the outcomes are orthogonal to the treatment assignment. This orthogonality constraint is then included in the loss function via a regularization. Based on our regularization framework, we develop deep orthogonal networks for unconfounded treatments (DONUT), which learn outcomes that are orthogonal to the treatment assignment. Using a variety of benchmark datasets for estimating average treatment effects, we demonstrate that DONUT outperforms the state-of-the-art substantially.

Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax rates of estimation have been established in recent years, many existing robust estimators with provably optimal convergence rates are also computationally intractable. In this paper, we study several estimation problems under a Wasserstein contamination model and present computationally tractable estimators motivated by generative adversarial networks (GANs). Specifically, we analyze properties of Wasserstein GAN-based estimators for location estimation, covariance matrix estimation, and linear regression and show that our proposed estimators are minimax optimal in many scenarios. Finally, we present numerical results which demonstrate the effectiveness of our estimators.

Interactive Educational Systems (IES) enabled researchers to trace student knowledge in different skills and provide recommendations for a better learning path. To estimate the student knowledge and further predict their future performance, the interest in utilizing the student interaction data captured by IES to develop learner performance models is increasing rapidly. Moreover, with the advances in computing systems, the amount of data captured by these IES systems is also increasing that enables deep learning models to compete with traditional logistic models and Markov processes. However, it is still not empirically evident if these deep models outperform traditional models on the current scale of datasets with millions of student interactions. In this work, we adopt EdNet, the largest student interaction dataset publicly available in the education domain, to understand how accurately both deep and traditional models predict future student performances. Our work observes that logistic regression models with carefully engineered features outperformed deep models from extensive experimentation. We follow this analysis with interpretation studies based on Locally Interpretable Model-agnostic Explanation (LIME) to understand the impact of various features on best performing model pre-dictions.

We basically train machines so as to include some kind of automation in it. In machine learning, we use various kinds of algorithms to allow machines to learn the relationships within the data provided and make predictions using them. So, the kind of model prediction where we need the predicted output is a continuous numerical value, it is called a regression problem. Regression analysis convolves around simple algorithms, which are often used in finance, investing, and others, and establishes the relationship between a single dependent variable dependent on several independent ones. For example, predicting house price or salary of an employee, etc are the most common regression problems.

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention to penalized regressions and ensemble of models. The nonlinear methods considered in the paper include shallow and deep neural networks, in their feed-forward and recurrent versions, and tree-based methods, such as random forests and boosted trees. We also consider ensemble and hybrid models by combining ingredients from different alternatives. Tests for superior predictive ability are briefly reviewed. Finally, we discuss application of machine learning in economics and finance and provide an illustration with high-frequency financial data.

Recent improvements in the predictive quality of natural language processing systems are often dependent on a substantial increase in the number of model parameters. This has led to various attempts of compressing such models, but existing methods have not considered the differences in the predictive power of various model components or in the generalizability of the compressed models. To understand the connection between model compression and out-of-distribution generalization, we define the task of compressing language representation models such that they perform best in a domain adaptation setting. We choose to address this problem from a causal perspective, attempting to estimate the \textit{average treatment effect} (ATE) of a model component, such as a single layer, on the model's predictions. Our proposed ATE-guided Model Compression scheme (AMoC), generates many model candidates, differing by the model components that were removed. Then, we select the best candidate through a stepwise regression model that utilizes the ATE to predict the expected performance on the target domain. AMoC outperforms strong baselines on 46 of 60 domain pairs across two text classification tasks, with an average improvement of more than 3\% in F1 above the strongest baseline.

Several deep neural ranking models have been proposed in the recent IR literature. While their transferability to one target domain held by a dataset has been widely addressed using traditional domain adaptation strategies, the question of their cross-domain transferability is still under-studied. We study here in what extent neural ranking models catastrophically forget old knowledge acquired from previously observed domains after acquiring new knowledge, leading to performance decrease on those domains. Our experiments show that the effectiveness of neuralIR ranking models is achieved at the cost of catastrophic forgetting and that a lifelong learning strategy using a cross-domain regularizer success-fully mitigates the problem. Using an explanatory approach built on a regression model, we also show the effect of domain characteristics on the rise of catastrophic forgetting. We believe that the obtained results can be useful for both theoretical and practical future work in neural IR.

Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints, is presented. Incorporating such information is particularly useful when the available data sets are small or do not cover the entire input space, as is often the case in manufacturing applications. The regression subject to the considered monotonicity constraints is set up as a semi-infinite optimization problem, and an adaptive solution algorithm is proposed. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It is tested and validated on two real-world manufacturing processes, namely laser glass bending and press hardening of sheet metal. It is found that the resulting models both comply well with the expert's monotonicity knowledge and predict the training data accurately. The suggested approach leads to lower root-mean-squared errors than comparative methods from the literature for the sparse data sets considered in this work.