Binyamin Perets

Mark Kozdoba, Binyamin Perets, Shie Mannor

We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While there is no closed analytic form for the associated kernel, we show that one can approximate it using sampling. The optimization problem needed to determine the density is non-convex, and standard gradient methods do not perform well. However, we show that with an appropriate initialization and using natural gradients, one can obtain well performing solutions. Finally, while the approach provides pre-densities (i.e. not necessarily integrating to 1), which prevents the use of log-likelihood for cross validation, we show that one can instead adapt Fisher divergence based score matching methods for this task. We evaluate the resulting method on the comprehensive recent anomaly detection benchmark suite, ADBench, and find that it ranks second best, among more than 15 algorithms.

Binyamin Perets, Mark Kozdoba, Shie Mannor

The Hidden Markov Model (HMM) is one of the most widely used statistical models for sequential data analysis. One of the key reasons for this versatility is the ability of HMM to deal with missing data. However, standard HMM learning algorithms rely crucially on the assumption that the positions of the missing observations \emph{within the observation sequence} are known. In the natural sciences, where this assumption is often violated, special variants of HMM, commonly known as Silent-state HMMs (SHMMs), are used. Despite their widespread use, these algorithms strongly rely on specific structural assumptions of the underlying chain, such as acyclicity, thus limiting the applicability of these methods. Moreover, even in the acyclic case, it has been shown that these methods can lead to poor reconstruction. In this paper we consider the general problem of learning an HMM from data with unknown missing observation locations. We provide reconstruction algorithms that do not require any assumptions about the structure of the underlying chain, and can also be used with limited prior knowledge, unlike SHMM. We evaluate and compare the algorithms in a variety of scenarios, measuring their reconstruction precision, and robustness under model miss-specification. Notably, we show that under proper specifications one can reconstruct the process dynamics as well as if the missing observations positions were known.

Mark Kozdoba, Binyamin Perets, Shie Mannor

There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning approaches, for a given method it may be non-trivial to decide whether the obtained fairness-performance curve of the method is optimal, i.e., whether it is close to the true Pareto front for these quantities for the underlying data distribution. In this paper we propose a new method to compute the optimal Pareto front, which does not require the training of complex representation models. We show that optimal fair representations possess several useful structural properties, and that these properties enable a reduction of the computation of the Pareto Front to a compact discrete problem. We then also show that these compact approximating problems can be efficiently solved via off-the shelf concave-convex programming methods. Since our approach is independent of the specific model of representations, it may be used as the benchmark to which representation learning algorithms may be compared. We experimentally evaluate the approach on a number of real world benchmark datasets.

Binyamin Perets, Shie Mannor

Large-scale hypothesis testing is central to modern science, where controlling the False Discovery Rate (FDR) has become the standard approach to managing false positives across many simultaneous tests. Hypotheses rarely exist in isolation; they often exhibit structure through proximity, connectivity, or hierarchy. This structure represents both a challenge and an opportunity: while classical methods treat these dependencies as obstacles requiring conservative correction, leveraging them can substantially increase discovery power. Here, we reframe structured FDR control as a regularized learning problem. By optimizing within a suitable Reproducing Kernel Hilbert Space (RKHS), we introduce a framework that unifies continuous domains, graphs, and hierarchies under a single algorithm through kernel choice alone. This formulation enables smooth solutions in place of the piecewise-constant fits of prior methods, principled likelihood-based hyperparameter selection rather than heuristic tuning, and inference at unobserved locations which in turn supports sample-efficient experimental design. Building on this estimator, we provide two decision rules which we prove to control the FDR. We validate our method on two sources: spatial locations derived from high-dimensional real-world datasets, and a differential gene expression task utilizing protein-protein interaction graphs.