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Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
Humans can often quickly and efficiently solve complex new learning tasks given only a small set of examples. In contrast, modern artificially intelligent systems often require thousands or millions of observations in order to solve even…
Subset selection is a valuable tool for interpretable learning, scientific discovery, and data compression. However, classical subset selection is often avoided due to selection instability, lack of regularization, and difficulties with…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…
Active learning is commonly used to train label-efficient models by adaptively selecting the most informative queries. However, most active learning strategies are designed to either learn a representation of the data (e.g., embedding or…
The cost and scarcity of fully supervised labels in statistical machine learning encourage using partially labeled data for model validation as a cheaper and more accessible alternative. Effectively collecting and leveraging weakly…
Unsupervised learning is the most challenging problem in machine learning and especially in deep learning. Among many scenarios, we study an unsupervised learning problem of high economic value --- learning to predict without costly pairing…
Selective prediction aims to learn a reliable model that abstains from making predictions when uncertain. These predictions can then be deferred to humans for further evaluation. As an everlasting challenge for machine learning, in many…
Using deep learning, we now have the ability to create exceptionally good semantic segmentation systems; however, collecting the prerequisite pixel-wise annotations for training images remains expensive and time-consuming. Therefore, it…
In several supervised learning scenarios, auxiliary losses are used in order to introduce additional information or constraints into the supervised learning objective. For instance, knowledge distillation aims to mimic outputs of a powerful…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
Active learning in semi-supervised classification involves introducing additional labels for unlabelled data to improve the accuracy of the underlying classifier. A challenge is to identify which points to label to best improve performance…
Representation learning aims to extract meaningful lower-dimensional embeddings from data, known as representations. Despite its widespread application, there is no established definition of a ``good'' representation. Typically, the…
Active learning aims to reduce the high labeling cost involved in training machine learning models on large datasets by efficiently labeling only the most informative samples. Recently, deep active learning has shown success on various…
In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack principled guarantees on coverage…
Subset selection for the rank $k$ approximation of an $n\times d$ matrix $A$ offers improvements in the interpretability of matrices, as well as a variety of computational savings. This problem is well-understood when the error measure is…