Antonio Blanca
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View article: A k-mer-based estimator of the substitution rate between repetitive sequences
A k-mer-based estimator of the substitution rate between repetitive sequences Open
K-mer-based analysis of genomic data is ubiquitous, but the presence of repetitive k-mers continues to pose problems for the accuracy of many methods. For example, the Mash tool (Ondov et al 2016) can accurately estimate the substitution r…
View article: Estimation of substitution and indel rates via <i>k</i>-mer statistics
Estimation of substitution and indel rates via <i>k</i>-mer statistics Open
Methods utilizing k -mers are widely used in bioinformatics, yet our understanding of their statistical properties under realistic mutation models remains incomplete. Previously, substitution-only mutation models have been considered to de…
View article: Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling
Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling Open
We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution \(\mu\) , an \(\varepsilon \gt 0\) , and access to sampling oracle(s) for a hidden distribution \(\pi\) , the goal in identit…
View article: Mean-field Potts and random-cluster dynamics from high-entropy initializations
Mean-field Potts and random-cluster dynamics from high-entropy initializations Open
A common obstruction to efficient sampling from high-dimensional distributions with Markov chains is the multimodality of the target distribution because they may get trapped far from stationarity. Still, one hopes that this is only a barr…
View article: On the tractability of sampling from the Potts model at low temperatures via random-cluster dynamics
On the tractability of sampling from the Potts model at low temperatures via random-cluster dynamics Open
Sampling from the $q$-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness ho…
View article: Rapid Mixing of Global Markov Chains via Spectral Independence: The Unbounded Degree Case
Rapid Mixing of Global Markov Chains via Spectral Independence: The Unbounded Degree Case Open
We consider spin systems on general n-vertex graphs of unbounded degree and explore the effects of spectral independence on the rate of convergence to equilibrium of global Markov chains. Spectral independence is a novel way of quantifying…
View article: Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling
Complexity of High-Dimensional Identity Testing with Coordinate Conditional Sampling Open
We study the identity testing problem for high-dimensional distributions. Given as input an explicit distribution $μ$, an $\varepsilon>0$, and access to sampling oracle(s) for a hidden distribution $π$, the goal in identity testing is to d…
View article: The critical mean-field Chayes–Machta dynamics
The critical mean-field Chayes–Machta dynamics Open
The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical fe…
View article: The minimizer Jaccard estimator is biased and inconsistent
The minimizer Jaccard estimator is biased and inconsistent Open
Motivation Sketching is now widely used in bioinformatics to reduce data size and increase data processing speed. Sketching approaches entice with improved scalability but also carry the danger of decreased accuracy and added bias. In this…
View article: Fast and perfect sampling of subgraphs and polymer systems
Fast and perfect sampling of subgraphs and polymer systems Open
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and wor…
View article: The Statistics of <i>k</i> -mers from a Sequence Undergoing a Simple Mutation Process Without Spurious Matches
The Statistics of <i>k</i> -mers from a Sequence Undergoing a Simple Mutation Process Without Spurious Matches Open
k-mer-based methods are widely used in bioinformatics, but there are many gaps in our understanding of their statistical properties. Here, we consider the simple model where a sequence S (e.g., a genome or a read) undergoes a simple mutati…
View article: The minimizer Jaccard estimator is biased and inconsistent*
The minimizer Jaccard estimator is biased and inconsistent* Open
Motivation Sketching is now widely used in bioinformatics to reduce data size and increase data processing speed. Sketching approaches entice with improved scalability but also carry the danger of decreased accuracy and added bias. In this…
View article: On mixing of Markov chains: coupling, spectral independence, and entropy factorization
On mixing of Markov chains: coupling, spectral independence, and entropy factorization Open
For general spin systems, we prove that a contractive coupling for an arbitrary local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dyn…
View article: Sampling from Potts on Random Graphs of Unbounded Degree via Random-Cluster Dynamics
Sampling from Potts on Random Graphs of Unbounded Degree via Random-Cluster Dynamics Open
We consider the problem of sampling from the ferromagnetic Potts and random-cluster models on a general family of random graphs via the Glauber dynamics for the random-cluster model. The random-cluster model is parametrized by an edge prob…
View article: On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization
On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization Open
For general spin systems, we prove that a contractive coupling for any local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, ar…
View article: The Critical Mean-field Chayes-Machta Dynamics
The Critical Mean-field Chayes-Machta Dynamics Open
The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical fe…
View article: The statistics of<i>k</i>-mers from a sequence undergoing a simple mutation process without spurious matches
The statistics of<i>k</i>-mers from a sequence undergoing a simple mutation process without spurious matches Open
K-mer-based methods are widely used in bioinformatics, but there are many gaps in our understanding of their statistical properties. Here, we consider the simple model where a sequence S (e.g. a genome or a read) undergoes a simple mutatio…
View article: The Swendsen-Wang Dynamics on Trees
The Swendsen-Wang Dynamics on Trees Open
The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. This chain has proved difficult to analyze, due in part to the global nature of…
View article: Random-cluster dynamics on random graphs in tree uniqueness.
Random-cluster dynamics on random graphs in tree uniqueness. Open
We establish rapid mixing of the random-cluster Glauber dynamics on random $\Delta$-regular graphs for all $q\ge 1$ and $p 2$ this threshold is sharp, and the Glauber dynamics on random $\Delta$-regular graphs undergoes an exponential slow…
View article: The Swendsen-Wang Dynamics on Trees
The Swendsen-Wang Dynamics on Trees Open
The Swendsen-Wang algorithm is a sophisticated, widely-used Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. This chain has proved difficult to analyze, due in part to the global nature of…
View article: Entropy decay in the Swendsen-Wang dynamics
Entropy decay in the Swendsen-Wang dynamics Open
We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is …
View article: Entropy decay in the Swendsen-Wang dynamics on ${\mathbb Z}^d$
Entropy decay in the Swendsen-Wang dynamics on ${\mathbb Z}^d$ Open
We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice ${\mathbb Z}^d$. This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is …
View article: Structure Learning of H-Colorings
Structure Learning of H-Colorings Open
We study the following structure learning problem for H -colorings. For a fixed (and known) constraint graph H with q colors, given access to uniformly random H -colorings of an unknown graph G=(V,E) , how many samples are required to lear…
View article: Hardness of Identity Testing for Restricted Boltzmann Machines and Potts models
Hardness of Identity Testing for Restricted Boltzmann Machines and Potts models Open
We study identity testing for restricted Boltzmann machines (RBMs), and more generally for undirected graphical models. Given sample access to the Gibbs distribution corresponding to an unknown or hidden model $M^*$ and given an explicit m…
View article: Random-cluster dynamics in $\mathbb{Z}^{2}$: Rapid mixing with general boundary conditions
Random-cluster dynamics in $\mathbb{Z}^{2}$: Rapid mixing with general boundary conditions Open
The random-cluster model with parameters $(p,q)$ is a random graph model that generalizes bond percolation ($q=1$) and the Ising and Potts models ($q\geq 2$). We study its Glauber dynamics on $n\times n$ boxes $Λ_{n}$ of the integer lattic…
View article: Swendsen‐Wang dynamics for general graphs in the tree uniqueness region
Swendsen‐Wang dynamics for general graphs in the tree uniqueness region Open
The Swendsen‐Wang (SW) dynamics is a popular Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph G = ( V , E ). The dynamics is conjectured to converge to equilibrium in O (| V | 1/4 ) steps a…
View article: Spatial mixing and nonlocal Markov chains
Spatial mixing and nonlocal Markov chains Open
We consider spin systems with nearest‐neighbor interactions on an n ‐vertex d ‐dimensional cube of the integer lattice graph . We study the effects that the strong spatial mixing condition (SSM) has on the rate of convergence to equilibriu…
View article: Lower bounds for testing graphical models: colorings and antiferromagnetic Ising models
Lower bounds for testing graphical models: colorings and antiferromagnetic Ising models Open
We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution $μ_{\hat{…
View article: Random-Cluster Dynamics in Z^2: Rapid Mixing with General Boundary Conditions
Random-Cluster Dynamics in Z^2: Rapid Mixing with General Boundary Conditions Open
The random-cluster (FK) model is a key tool for the study of phase transitions and for the design of efficient Markov chain Monte Carlo (MCMC) sampling algorithms for the Ising/Potts model. It is well-known that in the high-temperature reg…