Perfect Sampling for Hard Spheres from Strong Spatial Mixing

We provide a perfect sampling algorithm for the hard-sphere model on subsets of R^d with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling algorithms have been devised to sample from the hard-sphere model, and our perfect sampling algorithm is efficient for a range of parameters for which only efficient approximate samplers were previously known and is faster than these known approximate approaches. Our methods also extend to the more general setting of Gibbs point processes interacting via finite-range, repulsive potentials

A Spectral Independence View on Hard Spheres via Block Dynamics

The hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand-canonical partition function of the hard-sphere model in d dimensions. Up to a fugacity of ? < e/2^d, the runtime of our algorithm is polynomial in the volume of the system. This covers the entire known real-valued regime for the uniqueness of the Gibbs measure. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance we use clique dynamics, a Markov chain that was recently introduced in the setting of abstract polymer models. We prove rapid mixing of clique dynamics up to the tree threshold of the univariate hard-core model. This is achieved by relating clique dynamics to block dynamics and adapting the spectral expansion method, which was recently used to bound the mixing time of Glauber dynamics within the same parameter regime

bandt-pompe-master.zip

In this work, we propose a technique for the extraction and selection of relevant and non-redundant multivariate ordinal patterns from the high-dimensional combinatorial search space. Our proposed approach $ordex$, simultaneously extracts and scores the relevance and redundancy of ordinal patterns without training a classifier. As a filter-based approach, ordex aims to select a set of relevant patterns with complementary information. <br> Hence, using our scoring function based on the principles of Chebyshev's inequality, we maximize the relevance of the patterns and minimize the correlation between them. Our experiments on real-world datasets show that ordinality in time series contains valuable information for classification in several applications

Polymer dynamics via cliques: New conditions for approximations

International audienc

A Spectral Independence View on Hard Spheres via Block Dynamics

International audienceThe hard-sphere model is one of the most extensively studied models in statistical physics. It describes the continuous distribution of spherical particles, governed by hard-core interactions. An important quantity of this model is the normalizing factor of this distribution, called the partition function. We propose a Markov chain Monte Carlo algorithm for approximating the grand canonical partition function of the hard-sphere model in d dimensions. Up to a fugacity of \lambda < e/2 d , the runtime of our algorithm is polynomial in the volume of the system. Key to our approach is to define a discretization that closely approximates the partition function of the continuous model. This results in a discrete hard-core instance that is exponential in the size of the initial hard-sphere model. Our approximation bound follows directly from the correlation decay threshold of an infinite regular tree with degree equal to the maximum degree of our discretization. To cope with the exponential blow-up of the discrete instance, we use block dynamics, a Markov chain that generalizes the more frequently studied Glauber dynamics by grouping the vertices of the graph into blocks and updating an entire block instead of a single vertex in each step. We prove rapid mixing of block dynamics, based on disjoint cliques as blocks, up to the tree threshold of the univariate hard-core model. This is achieved by adapting the spectral expansion method, which was recently used for bounding the mixing time of Glauber dynamics within the same parameter regime

Counting and Sampling: Algorithms and Complexity (Dagstuhl Seminar 22482)

This report documents the program and the outcomes of Dagstuhl Seminar 22482 "Counting and Sampling: Algorithms and Complexity". We document the talks presented, covering many advances in the area made over the last five years. As well, we document the progress made by working groups on future projects

From Market Saturation to Social Reinforcement: Understanding the Impact of Non-Linearity in Information Diffusion Models

International audienc

The Irrelevance of Influencers: Information Diffusion with Re-Activation and Immunity Lasts Exponentially Long on Social Network Models

International audienceInformation diffusion models on networks are at the forefront of AI research. The dynamics of such models typically follow stochastic models from epidemiology, used to model not only infections but various phenomena, including the behavior of computer viruses and viral marketing campaigns. A core question in this setting is how to efficiently detect the most influential vertices in the host graph such that the infection survives the longest. In processes that incorporate re-infection of the vertices, such as the SIS process, theoretical studies identify parameter thresholds where the survival time of the process rapidly transitions from logarithmic to super-polynomial. These results contradict the intuition that the starting configuration is relevant, since the process will always either die out fast or survive almost indefinitely. A shortcoming of these results is that models incorporating short-term immunity (or creative advertisement fatigue) have not been subjected to such a theoretical analysis so far. We reduce this gap in the literature by studying the SIRS process, a more realistic model, which besides re-infection additionally incorporates short-term immunity. On complex network models, we identify parameter regimes for which the process survives exponentially long, and we get a tight threshold for random graphs. Underlying these results is our main technical contribution, showing a threshold behavior for the survival time of the SIRS process on graphs with large expander subgraphs, such as social network models