arXiv subjects

Federico Ciech

Publications and source records attributed to Federico Ciech.

4 recordsLinked to original sources

arXiv2021

Time Adaptive Gaussian Model

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim, we propose a novel method that leverages on Hidden Markov Models and Gaussian Graphical Models -- Time Adaptive Gaussian Model (TAGM). Our model is a generalization of state-of-the-art methods for the inference of temporal graphical models, its formulation leverages on both aspects of these models providing better results than current methods. In particular,it performs pattern recognition by clustering data points in time; and, it finds probabilistic (and possibly causal) relationships among the observed variables. Compared to current methods for temporal network inference, it reduces the basic assumptions while still showing good inference performances.

stat.ML↗

arXiv2018

A Large deviation principle for last passage times in an asymmetric Bernoulli potential

We prove a large deviation principle and give an expression for the rate function, for the last passage time in a Bernoulli environment. The model is exactly solvable and its invariant version satisfies a Burke-type property. Finally, we compute explicit limiting logarithmic moment generating functions for both the classical and the invariant models. The shape function of this model exhibits a flat edge in certain directions, and we also discuss the rate function and limiting log-moment generating functions in those directions.

math.PR↗

arXiv2018

Last passage percolation in an exponential environment with discontinuous rates

We prove a strong law of large numbers for directed last passage times in an independent but inhomogeneous exponential environment. Rates for the exponential random variables are obtained from a discretisation of a speed function that may be discontinuous on a locally finite set of discontinuity curves. The limiting shape is cast as a variational formula that maximises a certain functional over a set of weakly increasing curves. Using this result, we present two examples that allow for partial analytical tractability and show that the shape function may not be strictly concave, and it may exhibit points of non-differentiability, flat segments, and non-uniqueness of the optimisers of the variational formula. Finally, in a specific example, we analyse further the macroscopic optimisers and uncover a phase transition for their behaviour.

math.PR↗

arXiv2017

Order of the variance in the discrete Hammersley process with boundaries

We discuss the order of the variance on a lattice analogue of the Hammersley process with boundaries, for which the environment on each site has independent, Bernoulli distributed values. The last passage time is the maximum number of Bernoulli points that can be collected on a piecewise linear path, where each segment has strictly positive but finite slope. We show that along characteristic directions the order of the variance of the last passage time is of order $N^{2/3}$ in the model with boundary. These characteristic directions are restricted in a cone starting at the origin, and along any direction outside the cone, the order of the variance changes to $O(N)$ in the boundary model and to $O(1)$ for the non-boundary model. This behaviour is the result of the two flat edges of the shape function.

math.PR↗