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Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
We show that if G is a finite group and f is a {0,1}-valued function on G with Fourier algebra norm at most M then f may be computed by a coset decision tree (that is a decision tree in which at each vertex we query membership of a given…
We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the resulting tree should become shallower. We examine this…
In this paper, we provide a polynomial time algorithm to calculate the probability of a {\it ranked} gene tree topology for a given species tree, where a ranked tree topology is a tree topology with the internal vertices being ordered. The…
The paper tackles the power of randomization in the context of locality by analyzing the ability to`boost' the success probability of deciding a distributed language. The main outcome of this analysis is that the distributed computing…
Many high-stakes AI deployments proceed only if every stakeholder deems the system acceptable relative to their own minimum standard. With randomization over a finite menu of options, this becomes a feasibility question: does there exist a…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…
We prove a new lower bound on the parity decision tree complexity $\mathsf{D}_{\oplus}(f)$ of a Boolean function $f$. Namely, granularity of the Boolean function $f$ is the smallest $k$ such that all Fourier coefficients of $f$ are integer…
Guessing Random Additive Noise Decoding (GRAND) and its variants, known for their near-maximum likelihood performance, have been introduced in recent years. One such variant, Segmented GRAND, reduces decoding complexity by generating only…
Let R_eps denote randomized query complexity for error probability eps, and R:=R_{1/3}. In this work we investigate whether a perfect composition theorem R(f o g^n)=Omega(R(f).R(g)) holds for a relation f in {0,1}^n * S and a total inner…
Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances.…
Unreplicated two-level factorial designs are often used in screening experiments to determine which factors out of a large plausible set are active. A theorem regarding the generalized word count pattern is stated and proved for…
Efficient probabilistic inference by variable elimination in graphical models requires an optimal elimination order. However, finding an optimal order is a challenging combinatorial optimisation problem for models with a large number of…
Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been…
We present a randomized algorithm for reconstructing directed rooted trees of $n$ nodes and node degree at most $d$, by asking at most $O(dn\log^2 n)$ path queries. Each path query takes as input an origin node and a target node, and…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…