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Learning from data in the presence of outliers is a fundamental problem in statistics. Until recently, no computationally efficient algorithms were known to compute the mean of a high dimensional distribution under natural assumptions in…
Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced…
In this paper we consider the possibility of computing rather than training the decision layer weights of a neural classifier. Such a possibility arises in two way, from making an appropriate choice of loss function and by solving a problem…
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…
Functional relationships between objects, called `attributes', are of considerable importance in knowledge representation languages, including Description Logics (DLs). A study of the literature indicates that papers have made, often…
These lecture notes cover advanced topics in linear regression, with an in-depth exploration of the existence, uniqueness, relations, computation, and non-asymptotic properties of the most prominent estimators in this setting. The covered…
Euclidean embedding from noisy observations containing outlier errors is an important and challenging problem in statistics and machine learning. Many existing methods would struggle with outliers due to a lack of detection ability. In this…
The Projection Congruent Subset (PCS) Outlyingness is a new index of multivariate outlyingness obtained by considering univariate projections of the data. Like many other outlier detection procedures, PCS searches for a subset which…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
Additive models belong to the class of structured nonparametric regression models that do not suffer from the curse of dimensionality. Finding the additive components that are nonzero when the true model is assumed to be sparse is an…
Available data in machine learning applications is becoming increasingly complex, due to higher dimensionality and difficult classes. There exists a wide variety of approaches to measuring complexity of labeled data, according to class…
We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace. Finding a hidden subspace is known to be computationally hard. Nevertheless, using a non-proper…
The detection of influential observations for the standard least squares regression model is a question that has been extensively studied. LAD regression diagnostics offers alternative approaches whose main feature is the robustness. In…
This paper examines the problem of locating outlier columns in a large, otherwise low-rank matrix, in settings where {}{the data} are noisy, or where the overall matrix has missing elements. We propose a randomized two-step inference…
Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the…
The isolation forest algorithm for outlier detection exploits a simple yet effective observation: if taking some multivariate data and making uniformly random cuts across the feature space recursively, it will take fewer such random cuts…
User interaction data is an important source of supervision in counterfactual learning to rank (CLTR). Such data suffers from presentation bias. Much work in unbiased learning to rank (ULTR) focuses on position bias, i.e., items at higher…
Outlier detection and cleaning are essential steps in data preprocessing to ensure the integrity and validity of data analyses. This paper focuses on outlier points within individual trajectories, i.e., points that deviate significantly…
Recently, machine learning algorithms have successfully entered large-scale real-world industrial applications (e.g. search engines and email spam filters). Here, the CPU cost during test time must be budgeted and accounted for. In this…
We consider the problem of linear classification under general loss functions in the limited-data setting. Overfitting is a common problem here. The standard approaches to prevent overfitting are dimensionality reduction and regularization.…