Luigi Malagò

Principal Investigator Romanian Institute of Science and Technology - RIST Cluj-Napoca, Romania Address: Str. Cireşilor 29, 400487 Cluj-Napoca, Romania Email [my-last-name-without-any-accent]@rist.ro Office: +40 364 408794 My Google Scholar page |

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## Short Biography

Since July 2014 I'm Assistant Professor at Shinshu University in Nagano, and since October 2014, I will be a visiting research at Inria TAO in Paris for one year. Previously, from May to June 2014 I was a research assistant at Collegio Carlo Alberto, working with Giovanni Pistone. From April 2012 to April 2014, I was a postdoc researcher at the Department of Computer Science at Universita' degli Studi di Milano, working with Nicolo' Cesa-Bianchi. In 2012 I got a PhD in Computer Science Engineering at Politecnico di Milano, under the supervision of Matteo Matteucci and Giovanni Pistone, from Collegio Carlo Alberto, Moncalieri. During my PhD studies I had the opportunity to visit different laboratories. From April to July 2010 I have been a visiting researcher at MPI for Mathematics in the Sciences (MIS) in Leipzig, at Nihat Ay's group, and from July to August 2010 at Prof. Shun-ichi AMARI's lab, at RIKEN Brain Science Institute. Previosly, I obtained a Bachelor and a Master cum Laude in Computer Science Engineering at Politecnico di Milano, in 2004 and 2007, and a Diploma at Alta Scuola Politecnica in 2006. In 2012 I was awarded with the Dimitris N. Chorafas Foundation Award for best PhD thesis.

## Research Interests

My research interests focus on information geometry, and in particular on the study of stochastic optimization methods from a geometric perspective. I am also interested in machine learning, and in particular in online classification using selective sampling techniques.

#### Application of Information Geometry to Stochastic Optimization

Model-based optimization consists of a large family of optimization methods and algorithms where the search for the optimum is guided by the introduction of a stochastic model defined over the variables of the search space. The new objective function to be optimized becomes the stochastic relaxation of the objective function, i.e., the expected value of the original function with respect to a distribution in statistical model. From the point of view of information geometry, statistical models are Riemannian manifolds of probability distributions endowed with the Fisher information metric, thus given a statistical model, the stochastic relaxation becomes a continuos optimization problem defined over a differentiable manifold. The gradient descent techniques used to find the optimum of the stochastic relaxation which take into account the geometry of the new search space are based on the natural gradient, i.e., the gradient evaluated with respect to the Fisher information matrix. I'm interested in the study of stochastic optimization methods which perform Stochastic Natural Gradient Descent (SNGD), i.e., which approximate the natural gradient with a sample-based Monte Carlo estimation. I'm also interested in the second-order geometry of statistical models in the exponential family, based on the Riemannian Hessian, which allow to define second-order optimization methods over statistical manifolds.#### Online Learning with Selective Sampling

In online classification, the learner is provided with a sequence of observations which have to be classified online. After the prediction, the learner can access the label so that the classifier can be updated. In the selective sampling scenario, after the prediction the learner can chose whether or not to ask for the true label, in order to minimize the number of queries and at the same time obtain good prediction accuracies. I am interested in online classification algorithms with selective sampling in presence of multiple annotators, characterized by different costs and accuracies, where the learner has to chose not only when to ask for a label, but also which annotator to query.## Tutorials and Lectures

**Applications of Information Geometry to Combinatorial Optimization**at the PhD Course on Information Geometry in Learning and Optimization, Copenhagen, 22-26 September, 2014

Extra material: [animation]

## Publications

Selected papers appear in bold

#### Papers in Proceedings of International Journals

**Natural Gradient Flow in the Mixture Geometry of a Discrete Exponential Family.**

In Entropy 17(6), special issue on Information, Entropy and their Geometric Structures, 4215-4254, 2015

**Combinatorial Optimization with Information Geometry: Newton Method**.

In Entropy 16(8), special issue on Information Geometry, pages 4260-4289, 2014.

#### Papers in Proceedings of International Conferences

Second-Order Optimization over the Multivariate Gaussian Distribution.

In Geometric Science of Information GSI, 2015.

Information Geometry of Gaussian Distributions in View of Stochastic Optimization.

Proceedings of FOGA '15, held on January 17-20, 2015, Aberystwyth, Wales, 2015.

Gradient Flow of the Stochastic Relaxation on a Generic Exponential Family.

Proceedings of MaxEnt 2014, held on September 21-26, 2014, Château Clos Lucé, Amboise, France, 2014.

Extra material: [animation]

Optimization via Information Geometry.

In Book of Proceedings of the Seventh International Workshop on Simulation (IWS) held on May 21-25, 2013, in Rimini, Italy, 2014.

Robust Estimation of Natural Gradient in Optimization by Regularized Linear Regression.

In Geometric Science of Information GSI2013, 2013.

**Natural Gradient, Fitness Modelling and Model Selection: A Unifying Perspective**.

In IEEE Congress on Evolutionary Computation (CEC), 2013.

Variable Transformations in Estimation of Distribution Algorithms.

In Parallel Problem Solving from Nature - PPSN XII, Lecture Notes in Computer Science Volume 7491, pages 428--437, 2012.

Implicit Model Selection based on Variable Transformations in Estimation of Distribution.

In Learning and Intelligent OptimizatioN Conference LION 6, Lecture Notes in Computer Science, pages 360--365, 2012.

Optimization by l1-constrained Markov fitness modelling.

In Learning and Intelligent OptimizatioN Conference LION 6, Lecture Notes in Computer Science, pages 250--264, 2012.

Optimization of pseudo-boolean functions by stochastic natural gradient descent.

In MIC 2011, 9th Metaheuristics International Conference, 2011.

Introducing l1-regularized logistic regression in Markov networks based EDAs.

In Evolutionary Computation (CEC), 2011 IEEE Congress on, pages 1581--1588, 2011.

Stochastic natural gradient descent by estimation of empirical covariances.

In Evolutionary Computation (CEC), 2011 IEEE Congress on, pages 949--956, 2011.

**Towards the geometry of estimation of distribution algorithms based on the exponential family**.

In Proceedings of FOGA '11, pages 230--242, New York, NY, USA, 2011. ACM.

Evoptool: An extensible toolkit for evolutionary optimization algorithms comparison.

In Evolutionary Computation (CEC), 2010 IEEE Congress on, pages 1--8, 2010.

Milan Robocup Team 2009.

Robocup International Symposium 2009, Robocup 2009, Graz, Austria, pages 1--8, 2009.

#### Papers in Workshops

**.**

Online Active Learning with Strong and Weak Annotators

Online Active Learning with Strong and Weak Annotators

NIPS 2014 Workshop on Crowdsourcing and Machine Learning, Montreal, Canada, 13 December 2014.

Stochastic Relaxation over the Exponential Family: Second-Order Geometry.

NIPS 2014 Workshop on Optimization for Machine Learning (OPT2014), Montreal, Canada, 12 December 2014.

A note on the border of an exponential family.

Working paper, Carlo Alberto Notebooks, No. 168. A shorter version of the paper was presented at the SIS 2010 conference in Padova, Italy. [arXiv:1012.0637]

Stochastic relaxation as a unifying approach in 0/1 programming.

NIPS 2009 Workshop on Discrete Optimization in Machine Learning: Submodularity, Sparsity & Polyhedra (DISCML), Whistler, Canada, 2009.

An information geometry perspective on estimation of distribution algorithms: boundary analysis.

In Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation, GECCO '08, pages 2081--2088, New York, NY, USA, 2008. ACM.

#### Other contributions

IERoKi, Innovative Entertainment Robot for Kids.

In Multidisciplinarity and Innovation, ASP projects 1, Alta Scuola Politecnica, pages 56--59. Telesma Edizioni, 2007.

Extra material: [video]

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Last update 14 September 2016