相关论文: Combinatorial perspectives on Dollo-$k$ characters…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
Reconstructing the evolutionary history of a set of species is a central task in computational biology. In real data, it is often the case that some information is missing: the Incomplete Directed Perfect Phylogeny (IDPP) problem asks,…
In this paper, we address the problem of discriminative dictionary learning (DDL), where sparse linear representation and classification are combined in a probabilistic framework. As such, a single discriminative dictionary and linear…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
We introduce a new metric of match, called Cartesian tree matching, which means that two strings match if they have the same Cartesian trees. Based on Cartesian tree matching, we define single pattern matching for a text of length n and a…
When samples have internal structure, we often see a mismatch between the objective optimized during training and the model's goal during inference. For example, in sequence-to-sequence modeling we are interested in high-quality translated…
We establish a log-supermodularity property for probability distributions on binary patterns observed at the tips of a tree that are generated under any 2--state Markov process. We illustrate the applicability of this result in…
Machine and deep learning have grown in popularity and use in biological research over the last decade but still present challenges in interpretability of the fitted model. The development and use of metrics to determine features driving…
The explosive growth of large language models (LLMs) has created a vast but opaque landscape: millions of models exist, yet their evolutionary relationships through fine-tuning, distillation, or adaptation are often undocumented or unclear,…
Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity…
In this work we deal with parameter estimation in a latent variable model, namely the multiple-hidden i.i.d. model, which is derived from multiple alignment algorithms. We first provide a rigorous formalism for the homology structure of k…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…
Given two phylogenetic trees on the same set of taxa X, the maximum parsimony distance d_MP is defined as the maximum, ranging over all characters c on X, of the absolute difference in parsimony score induced by c on the two trees. In this…
Spike sorting is a class of algorithms used in neuroscience to attribute the time occurences of particular electric signals, called action potential or spike, to neurons. We rephrase this problem as a particular optimization problem : Lasso…
Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change…
We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good…