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As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
Statistical learning is the process of estimating an unknown probabilistic input-output relationship of a system using a limited number of observations. A statistical learning machine (SLM) is the algorithm, function, model, or rule, that…
The use of machine learning to develop intelligent software tools for interpretation of radiology images has gained widespread attention in recent years. The development, deployment, and eventual adoption of these models in clinical…
Artificial intelligence has made remarkable progress in handling complex tasks, thanks to advances in hardware acceleration and machine learning algorithms. However, to acquire more accurate outcomes and solve more complex issues,…
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the…
Modern data and applications pose very different challenges from those of the 1950s or even the 1980s. Students contemplating a career in statistics or data science need to have the tools to tackle problems involving massive, heavy-tailed…
A key problem in deep learning and computational neuroscience is relating the geometrical properties of neural representations to task performance. Here, we consider this problem for continuous decoding tasks where neural variability may…
Electromagnetic phenomena are mathematically described by solutions of boundary value problems. For exploiting symmetries of these boundary value problems in a way that is offered by techniques of dimensional reduction, it needs to be…
Numerous deep learning architectures have been developed to accommodate the diversity of time series datasets across different domains. In this article, we survey common encoder and decoder designs used in both one-step-ahead and…
Deep learning algorithms vary depending on the underlying connection mechanism of nodes of them. They have various hyperparameters that are either set via specific algorithms or randomly chosen. Meanwhile, hyperparameters of deep learning…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…
We study the typical properties of polynomial Support Vector Machines within a Statistical Mechanics approach that allows us to analyze the effect of different normalizations of the features. If the normalization is adecuately chosen, there…
Hacking and false data injection from adversaries can threaten power grids' everyday operations and cause significant economic loss. Anomaly detection in power grids aims to detect and discriminate anomalies caused by cyber attacks against…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
The theory of statistical learning has focused on variational objectives expressed on functions. In this note, we discuss motivations to write similar objectives on measures, in particular to discuss out-of-distribution generalization and…
Machine learning, a branch of artificial intelligence, learns from previous experience to optimize performance, which is ubiquitous in various fields such as computer sciences, financial analysis, robotics, and bioinformatics. A challenge…
Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…
The big data trend has inspired feature-driven learning tasks, which cannot be handled by conventional machine learning models. Unstructured data produces very large binary matrices with millions of columns when converted to vector form.…