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Today, data analysts largely rely on intuition to determine whether missing or withheld rows of a dataset significantly affect their analyses. We propose a framework that can produce automatic contingency analysis, i.e., the range of values…
The missing data problem has been broadly studied in the last few decades and has various applications in different areas such as statistics or bioinformatics. Even though many methods have been developed to tackle this challenge, most of…
We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…
Missing data imputation, where a model is trained on observed data to estimate unobserved values, is a fundamental problem in machine learning. In this paper, we rigorously formulate imputation model learning as a mean-squared error risk…
This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…
This paper applies the minimum message length principle to inference of linear regression models with Student-t errors. A new criterion for variable selection and parameter estimation in Student-t regression is proposed. By exploiting…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
Datasets with missing values are very common on industry applications, and they can have a negative impact on machine learning models. Recent studies introduced solutions to the problem of imputing missing values based on deep generative…
We analyze the best achievable performance of Bayesian learning under generative models by defining and upper-bounding the minimum excess risk (MER): the gap between the minimum expected loss attainable by learning from data and the minimum…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
A fundamental principle of learning theory is that there is a trade-off between the complexity of a prediction rule and its ability to generalize. Modern machine learning models do not obey this paradigm: They produce an accurate prediction…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…
We investigate methods for penalized regression in the presence of missing observations. This paper introduces a method for estimating the parameters which compensates for the missing observations. We first, derive an unbiased estimator of…
Learning models that can handle distribution shifts is a key challenge in domain generalization. Invariance learning, an approach that focuses on identifying features invariant across environments, improves model generalization by capturing…
Heterogeneous but complementary sources of data provide an unprecedented opportunity for developing accurate statistical models of systems. Although the existing methods have shown promising results, they are mostly applicable to situations…
We consider learning methods based on the regularization of a convex empirical risk by a squared Hilbertian norm, a setting that includes linear predictors and non-linear predictors through positive-definite kernels. In order to go beyond…
For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
Missing data are a common problem for both the construction and implementation of a prediction algorithm. Pattern mixture kernel submodels (PMKS) - a series of submodels for every missing data pattern that are fit using only data from that…