# Francesco Locatello, MSc. ETH Computer Science

“R2D2, you know better than to trust a strange computer! - cit. C3PO”

# PhD Student

E-Mail
locatelf@ethz.ch
Phone
+41 44 632 23 74
ETH Zürich
Department of Computer Science
Biomedical Informatics Group Universitätsstrasse 6
CAB F52.2
8092 Zürich
Room
CAB F52.2

My research focuses on constrained greedy optimization and boosting.

I graduated cum laude from the university of Padua in Information Engineering and then joined ETH for my master in Computer Science. During this time I became passionate about Machine Learning and I am now part of the Max Planck-ETH Center for Learning Systems, supervised by Gunnar Rätsch and Bernhard Schölkopf. I am very passionate about optimization for machine learning.

#### Francesco Locatello, Anant Raj, Sai Praneeth Reddy, Gunnar Rätsch, Bernhard Schölkopf, Sebastian U Stich, Martin Jaggi On Matching Pursuit and Coordinate Descent ICML 2018

Abstract Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $O(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $O(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

Authors Francesco Locatello, Anant Raj, Sai Praneeth Reddy, Gunnar Rätsch, Bernhard Schölkopf, Sebastian U Stich, Martin Jaggi

Submitted ICML 2018

#### Alp Yurtsever, Olivier Fercoq, Francesco Locatello, Volkan Cevher A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming ICML 2018

Abstract We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines the notions of smoothing and homotopy under the CGM framework, and provably achieves the optimal $\mathcal {O}(1/\sqrt {k})$ convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. Specific applications of the framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. We provide numerical evidence to demonstrate the benefits of the new framework.

Authors Alp Yurtsever, Olivier Fercoq, Francesco Locatello, Volkan Cevher

Submitted ICML 2018

#### Vincent Fortuin, Matthias Hüser, Francesco Locatello, Heiko Strathmann, Gunnar Rätsch Deep Self-Organization: Interpretable Discrete Representation Learning on Time Series arXiv Preprints

Abstract Human professionals are often required to make decisions based on complex multivariate time series measurements in an online setting, e.g. in health care. Since human cognition is not optimized to work well in high-dimensional spaces, these decisions benefit from interpretable low-dimensional representations. However, many representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose to couple a variational autoencoder to a discrete latent space and introduce a topological structure through the use of self-organizing maps. This allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the latent space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application. In the latter experiment, our representation uncovers meaningful structure in the acute physiological state of a patient.

Authors Vincent Fortuin, Matthias Hüser, Francesco Locatello, Heiko Strathmann, Gunnar Rätsch

Submitted arXiv Preprints

#### Francesco Locatello, Damien Vincent, Ilya Tolstikhin, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf Clustering Meets Implicit Generative Models Arxiv

Abstract Clustering is a cornerstone of unsupervised learning which can be thought as disentangling the multiple generative mechanisms underlying the data. In this paper we introduce an algorithmic framework to train mixtures of implicit generative models which we instantiate for variational autoencoders. Relying on an additional set of discriminators, we propose a competitive procedure in which the models only need to approximate the portion of the data distribution from which they can produce realistic samples. As a byproduct, each model is simpler to train, and a clustering interpretation arises naturally from the partitioning of the training points among the models. We empirically show that our approach splits the training distribution in a reasonable way and increases the quality of the generated samples.

Authors Francesco Locatello, Damien Vincent, Ilya Tolstikhin, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf

Submitted Arxiv

#### Francesco Locatello, Rajiv Khanna, Joydeep Ghosh, Gunnar Rätsch Boosting Variational Inference: an Optimization Perspective AISTATS 2018

Abstract Variational Inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, Boosting Variational Inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. In the present work, we study the convergence properties of this approach from a modern optimization viewpoint by establishing connections to the classic Frank-Wolfe algorithm. Our analyses yields novel theoretical insights on the Boosting of Variational Inference regarding the sufficient conditions for convergence, explicit sublinear/linear rates, and algorithmic simplifications.

Authors Francesco Locatello, Rajiv Khanna, Joydeep Ghosh, Gunnar Rätsch

Submitted AISTATS 2018

#### Francesco Locatello, Michael Tschannen, Gunnar Rätsch, Martin Jaggi Greedy Algorithms for Cone Constrained Optimization with Convergence Guarantees NIPS 2017

Abstract Greedy optimization methods such as Matching Pursuit (MP) and Frank-Wolfe (FW) algorithms regained popularity in recent years due to their simplicity, effectiveness and theoretical guarantees. MP and FW address optimization over the linear span and the convex hull of a set of atoms, respectively. In this paper, we consider the intermediate case of optimization over the convex cone, parametrized as the conic hull of a generic atom set, leading to the first principled definitions of non-negative MP algorithms for which we give explicit convergence rates and demonstrate excellent empirical performance. In particular, we derive sublinear (O(1/t)) convergence on general smooth and convex objectives, and linear convergence (O(e−t)) on strongly convex objectives, in both cases for general sets of atoms. Furthermore, we establish a clear correspondence of our algorithms to known algorithms from the MP and FW literature. Our novel algorithms and analyses target general atom sets and general objective functions, and hence are directly applicable to a large variety of learning settings.

Authors Francesco Locatello, Michael Tschannen, Gunnar Rätsch, Martin Jaggi

Submitted NIPS 2017

#### Francesco Locatello, Rajiv Khanna, Michael Tschannen, Martin Jaggi A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe AISTATS 2017

Abstract Two of the most fundamental prototypes of greedy optimization are the matching pursuit and FrankWolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching pursuit methods in an optimization sense, for general sets of atoms. We derive sublinear (1/t) convergence for both classes on general smooth objectives, and linear convergence on strongly convex objectives, as well as a clear correspondence of algorithm variants. Our presented algorithms and rates are affine invariant, and do not need any incoherence or sparsity assumptions.

Authors Francesco Locatello, Rajiv Khanna, Michael Tschannen, Martin Jaggi

Submitted AISTATS 2017