arXiv subjects

Blazej Miasojedow

Publications and source records attributed to Blazej Miasojedow.

11 recordsLinked to original sources

arXiv2021

Predicting the redshift of gamma-ray loud AGNs using supervised machine learning

AGNs are very powerful galaxies characterized by extremely bright emissions coming out from their central massive black holes. Knowing the redshifts of AGNs provides us with an opportunity to determine their distance to investigate important astrophysical problems such as the evolution of the early stars, their formation along with the structure of early galaxies. The redshift determination is challenging because it requires detailed follow-up of multi-wavelength observations, often involving various astronomical facilities. Here, we employ machine learning algorithms to estimate redshifts from the observed gamma-ray properties and photometric data of gamma-ray loud AGN from the Fourth Fermi-LAT Catalog. The prediction is obtained with the Superlearner algorithm, using LASSO selected set of predictors. We obtain a tight correlation, with a Pearson Correlation Coefficient of 71.3% between the inferred and the observed redshifts, an average Δz_norm = 11.6 x 10^-4. We stress that notwithstanding the small sample of gamma-ray loud AGNs, we obtain a reliable predictive model using Superlearner, which is an ensemble of several machine learning models.

astro-ph.HE↗

arXiv2019

Adaptive Bayesian SLOPE -- High-dimensional Model Selection with Missing Values

We consider the problem of variable selection in high-dimensional settings with missing observations among the covariates. To address this relatively understudied problem, we propose a new synergistic procedure -- adaptive Bayesian SLOPE -- which effectively combines the SLOPE method (sorted $l_1$ regularization) together with the Spike-and-Slab LASSO method. We position our approach within a Bayesian framework which allows for simultaneous variable selection and parameter estimation, despite the missing values. As with the Spike-and-Slab LASSO, the coefficients are regarded as arising from a hierarchical model consisting of two groups: (1) the spike for the inactive and (2) the slab for the active. However, instead of assigning independent spike priors for each covariate, here we deploy a joint "SLOPE" spike prior which takes into account the ordering of coefficient magnitudes in order to control for false discoveries. Through extensive simulations, we demonstrate satisfactory performance in terms of power, FDR and estimation bias under a wide range of scenarios. Finally, we analyze a real dataset consisting of patients from Paris hospitals who underwent a severe trauma, where we show excellent performance in predicting platelet levels. Our methodology has been implemented in C++ and wrapped into an R package ABSLOPE for public use.

stat.ME↗

arXiv2019

Gamma-ray Bursts as distance indicators through a machine learning approach

Gamma-ray bursts (GRBs) are spectacularly energetic events, with the potential to inform on the early universe and its evolution, once their redshifts are known. Unfortunately, determining redshifts is a painstaking procedure requiring detailed follow-up multi-wavelength observations often involving various astronomical facilities, which have to be rapidly pointed at these serendipitous events. Here we use Machine Learning algorithms to infer redshifts from a collection of observed temporal and spectral features of GRBs. We obtained a very high correlation coefficient ($0.96$) between the inferred and the observed redshifts, and a small dispersion (with a mean square error of $0.003$) in the test set. The addition of plateau afterglow parameters improves the predictions by $61.4\%$ compared to previous results. The GRB luminosity function and cumulative density rate evolutions, obtained from predicted and observed redshift are in excellent agreement indicating that GRBs are effective distance indicators and a reliable step for the cosmic distance ladder.

astro-ph.HE↗

arXiv2019

Non-asymptotic Analysis of Biased Stochastic Approximation Scheme

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions such as unbiased gradient estimates and convex objective function, which significantly limit their applications to sophisticated tasks such as online and reinforcement learning. These restrictions are all essentially relaxed in this work. In particular, we analyze a general SA scheme to minimize a non-convex, smooth objective function. We consider update procedure whose drift term depends on a state-dependent Markov chain and the mean field is not necessarily of gradient type, covering approximate second-order method and allowing asymptotic bias for the one-step updates. We illustrate these settings with the online EM algorithm and the policy-gradient method for average reward maximization in reinforcement learning.

stat.ML↗

arXiv2015

Particle Gibbs algorithms for Markov jump processes

In the present paper we propose a new MCMC algorithm for sampling from the posterior distribution of hidden trajectory of a Markov jump process. Our algorithm is based on the idea of exploiting virtual jumps, introduced by Rao and Teh (2013). The main novelty is that our algorithm uses particle Gibbs with ancestor sampling to update the skeleton, while Rao and Teh use forward filtering backward sampling (FFBS). In contrast to previous methods our algorithm can be implemented even if the state space is infinite. In addition, the cost of a single step of the proposed algorithm does not depend on the size of the state space. The computational cost of our methood is of order $\mathcal{O}(N\mathbb{E}(n))$, where $N$ is the number of particles used in the PGAS algorithm and $\mathbb{E}(n)$ is the expected number of jumps (together with virtual ones). The cost of the algorithm of Rao and Teh is of order $\mathcal{O}(|\mathcal{X}|^2\mathbb{E}(n))$, where $|\mathcal{X}|$ is the size of the state space. Simulation results show that our algorithm with PGAS converges slightly slower than the algorithm with FFBS, if the size of the state space is not big. However, if the size of the state space increases, the proposed method outperforms existing ones. We give special attention to a hierarchical version of our algorithm which can be applied to continuous time Bayesian networks (CTBNs).

stat.CO↗

arXiv2014

Asymptotics of Monte Carlo maximum likelihood estimators

We describe Monte Carlo approximation to the maximum likelihood estimator in models with intractable norming constants and explanatory variables. We consider both sources of randomness (due to the initial sample and to Monte Carlo simulations) and prove asymptotical normality of the estimator.

stat.ME↗

arXiv2014

Adaptive Monte Carlo Maximum Likelihood

We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We examine asymptotics of adaptive importance sampling and a new algorithm, which uses resampling and MCMC. This algorithm is designed to reduce problems with degeneracy of importance weights. Our analysis is based on martingale limit theorems. We also describe how adaptive maximization algorithms of Newton-Raphson type can be combined with the resampling techniques. The paper includes results of a small scale simulation study in which we compare the performance of adaptive and non-adaptive Monte Carlo maximum likelihood algorithms.

stat.ME↗

arXiv2014

Metropolis-type algorithms for Continuous Time Bayesian Networks

We present a Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm for detecting hidden variables in a continuous time Bayesian network (CTBN), which uses reversible jumps in the sense defined by (Green 1995). In common with several Monte Carlo algorithms, one of the most recent and important by (Rao and Teh 2013), our algorithm exploits uniformization techniques under which a continuous time Markov process can be represented as a marked Poisson process. We exploit this in a novel way. We show that our MCMC algorithm can be more efficient than those of likelihood weighting type, as in (Nodelman et al. 2003) and (Fan et al. 2010) and that our algorithm broadens the class of important examples that can be treated effectively.

stat.ME↗

arXiv2012

Adaptive parallel tempering algorithm

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kind of scenarios without prior tuning.

stat.CO↗

arXiv2011

Nonasymptotic bounds on the mean square error for MCMC estimates via renewal techniques

The Nummellin's split chain construction allows to decompose a Markov chain Monte Carlo (MCMC) trajectory into i.i.d. "excursions". RegenerativeMCMC algorithms based on this technique use a random number of samples. They have been proposed as a promising alternative to usual fixed length simulation [25, 33, 14]. In this note we derive nonasymptotic bounds on the mean square error (MSE) of regenerative MCMC estimates via techniques of renewal theory and sequential statistics. These results are applied to costruct confidence intervals. We then focus on two cases of particular interest: chains satisfying the Doeblin condition and a geometric drift condition. Available explicit nonasymptotic results are compared for different schemes of MCMC simulation.

stat.CO↗

arXiv2009

Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. We also consider confidence bounds. We first derive the results in terms of the asymptotic variance and then bound the asymptotic variance for both uniformly ergodic and geometrically ergodic Markov chains.

stat.ME↗