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We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…
Error bounds and complexity bounds in numerical analysis and information-based complexity are often proved for functions that are defined on very simple domains, such as a cube, a torus, or a sphere. We study optimal error bounds for the…
The arrival of AI techniques in computations, with the potential for hallucinations and non-robustness, has made trustworthiness of algorithms a focal point. However, trustworthiness of the many classical approaches are not well understood.…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
We study the phase diagram and the algorithmic hardness of the random `locked' constraint satisfaction problems, and compare them to the commonly studied 'non-locked' problems like satisfiability of boolean formulas or graph coloring. The…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
We propose a planning and control approach to physics-based manipulation. The key feature of the algorithm is that it can adapt to the accuracy requirements of a task, by slowing down and generating `careful' motion when the task requires…
Accurate uncertainty estimates are important in sequential model-based decision-making tasks such as Bayesian optimization. However, these estimates can be imperfect if the data violates assumptions made by the model (e.g., Gaussianity).…
Motivated by a plethora of practical examples where bias is induced by automated-decision making algorithms, there has been strong recent interest in the design of fair algorithms. However, there is often a dichotomy between fairness and…
Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms typically converge only to a single solution. While this can be counteracted by applying niching…
Dataset bias is one of the prevailing causes of unfairness in machine learning. Addressing fairness at the data collection and dataset preparation stages therefore becomes an essential part of training fairer algorithms. In particular,…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize…
This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…
To reduce human error and prejudice, many high-stakes decisions have been turned over to machine algorithms. However, recent research suggests that this does not remove discrimination, and can perpetuate harmful stereotypes. While…
Objective: This paper develops a theoretical framework explaining when and why AI explanations enhance versus impair human decision-making. Background: Transparency is advocated as universally beneficial for human-AI interaction, yet…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often…
Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the…