# Francesco Locatello, MSc. ETH Computer Science

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

# Alumni

E-Mail
locatelf@ethz.ch

I am interested in representation learning and causality. Before, I also worked on convex optimization and Bayesian inference.

I am a doctoral fellow of the Max Planck-ETH Center for Learning Systems and ELLIS, supervised by Gunnar Rätsch and Bernhard Schölkopf. Before, I graduated cum laude from the University of Padua in Information Engineering and then joined ETH for my master in Computer Science. I hold a Google PhD Fellowship in Machine Learning, received the best paper award at the International Conference of Machine Learning (ICML) 2019, and the ISBA@NIPS award at Advances in Approximate Bayesian Inference Workshop NIPS 2017. I was part of the organizing team of the NeurIPS 2019 challenge: "Disentanglement: From Simulation to Real-World". During my PhD I worked part-time as a research consultant for ETH and MPI (in collaboration with Google Research, Brain Team, Zurich) and interned in Google Research, Brain Team Amsterdam.

#### Hugo Yèche, Gideon Dresdner, Francesco Locatello, Matthias Hüser, Gunnar Rätsch Neighborhood Contrastive Learning Applied to Online Patient Monitoring ICML 2021

Abstract Intensive care units (ICU) are increasingly looking towards machine learning for methods to provide online monitoring of critically ill patients. In machine learning, online monitoring is often formulated as a supervised learning problem. Recently, contrastive learning approaches have demonstrated promising improvements over competitive supervised benchmarks. These methods rely on well-understood data augmentation techniques developed for image data which do not apply to online monitoring. In this work, we overcome this limitation by supplementing time-series data augmentation techniques with a novel contrastive learning objective which we call neighborhood contrastive learning (NCL). Our objective explicitly groups together contiguous time segments from each patient while maintaining state-specific information. Our experiments demonstrate a marked improvement over existing work applying contrastive methods to medical time-series.

Authors Hugo Yèche, Gideon Dresdner, Francesco Locatello, Matthias Hüser, Gunnar Rätsch

Submitted ICML 2021

#### Stefan G Stark, Joanna Ficek, Francesco Locatello, Ximena Bonilla, Stéphane Chevrier, Franziska Singer, Tumor Profiler Consortium, Gunnar Rätsch, Kjong-Van Lehmann SCIM: universal single-cell matching with unpaired feature sets Bioinformatics

Abstract Motivation Recent technological advances have led to an increase in the production and availability of single-cell data. The ability to integrate a set of multi-technology measurements would allow the identification of biologically or clinically meaningful observations through the unification of the perspectives afforded by each technology. In most cases, however, profiling technologies consume the used cells and thus pairwise correspondences between datasets are lost. Due to the sheer size single-cell datasets can acquire, scalable algorithms that are able to universally match single-cell measurements carried out in one cell to its corresponding sibling in another technology are needed. Results We propose Single-Cell data Integration via Matching (SCIM), a scalable approach to recover such correspondences in two or more technologies. SCIM assumes that cells share a common (low-dimensional) underlying structure and that the underlying cell distribution is approximately constant across technologies. It constructs a technology-invariant latent space using an autoencoder framework with an adversarial objective. Multi-modal datasets are integrated by pairing cells across technologies using a bipartite matching scheme that operates on the low-dimensional latent representations. We evaluate SCIM on a simulated cellular branching process and show that the cell-to-cell matches derived by SCIM reflect the same pseudotime on the simulated dataset. Moreover, we apply our method to two real-world scenarios, a melanoma tumor sample and a human bone marrow sample, where we pair cells from a scRNA dataset to their sibling cells in a CyTOF dataset achieving 90% and 78% cell-matching accuracy for each one of the samples, respectively.

Authors Stefan G Stark, Joanna Ficek, Francesco Locatello, Ximena Bonilla, Stéphane Chevrier, Franziska Singer, Tumor Profiler Consortium, Gunnar Rätsch, Kjong-Van Lehmann

Submitted Bioinformatics

#### Francesco Locatello, Dirk Weissenborn, Thomas Unterthiner, Aravindh Mahendran, Georg Heigold, Jakob Uszkoreit, Alexey Dosovitskiy, Thomas Kipf Object-Centric Learning with Slot Attention NeurIPS 2020 (spotlight)

Abstract Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-level perceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes. In this paper, we present the Slot Attention module, an architectural component that interfaces with perceptual representations such as the output of a convolutional neural network and produces a set of task-dependent abstract representations which we call slots. These slots are exchangeable and can bind to any object in the input by specializing through a competitive procedure over multiple rounds of attention. We empirically demonstrate that Slot Attention can extract object-centric representations that enable generalization to unseen compositions when trained on unsupervised object discovery and supervised property prediction tasks.

Authors Francesco Locatello, Dirk Weissenborn, Thomas Unterthiner, Aravindh Mahendran, Georg Heigold, Jakob Uszkoreit, Alexey Dosovitskiy, Thomas Kipf

Submitted NeurIPS 2020 (spotlight)

#### Geoffrey Négiar, Gideon Dresdner, Alicia Tsai, Laurent El Ghaoui, Francesco Locatello, Robert M. Freund, Fabian Pedregosa Stochastic Frank-Wolfe for Constrained Finite-Sum Minimization ICML 2020

Abstract We propose a novel Stochastic Frank-Wolfe (a.k.a. conditional gradient) algorithm for constrained smooth finite-sum minimization with a generalized linear prediction/structure. This class of problems includes empirical risk minimization with sparse, low-rank, or other structured constraints. The proposed method is simple to implement, does not require step-size tuning, and has a constant per-iteration cost that is independent of the dataset size. Furthermore, as a byproduct of the method we obtain a stochastic estimator of the Frank-Wolfe gap that can be used as a stopping criterion. Depending on the setting, the proposed method matches or improves on the best computational guarantees for Stochastic Frank-Wolfe algorithms. Benchmarks on several datasets highlight different regimes in which the proposed method exhibits a faster empirical convergence than related methods. Finally, we provide an implementation of all considered methods in an open-source package.

Authors Geoffrey Négiar, Gideon Dresdner, Alicia Tsai, Laurent El Ghaoui, Francesco Locatello, Robert M. Freund, Fabian Pedregosa

Submitted ICML 2020

#### Francesco Locatello, Ben Poole, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem, Michael Tschannen Weakly-Supervised Disentanglement without Compromises ICML 2020

Abstract Intelligent agents should be able to learn useful representations by observing changes in their environment. We model such observations as pairs of non-i.i.d. images sharing at least one of the underlying factors of variation. First, we theoretically show that only knowing how many factors have changed, but not which ones, is sufficient to learn disentangled representations. Second, we provide practical algorithms that learn disentangled representations from pairs of images without requiring annotation of groups, individual factors, or the number of factors that have changed. Third, we perform a large-scale empirical study and show that such pairs of observations are sufficient to reliably learn disentangled representations on several benchmark data sets. Finally, we evaluate our learned representations and find that they are simultaneously useful on a diverse suite of tasks, including generalization under covariate shifts, fairness, and abstract reasoning. Overall, our results demonstrate that weak supervision enables learning of useful disentangled representations in realistic scenarios.

Authors Francesco Locatello, Ben Poole, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem, Michael Tschannen

Submitted ICML 2020

#### Francesco Locatello, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, Olivier Bachem A Commentary on the Unsupervised Learning of Disentangled Representations AAAI 2020

Abstract The goal of the unsupervised learning of disentangled representations is to separate the independent explanatory factors of variation in the data without access to supervision. In this paper, we summarize the results of Locatello et al., 2019, and focus on their implications for practitioners. We discuss the theoretical result showing that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases and the practical challenges it entails. Finally, we comment on our experimental findings, highlighting the limitations of state-of-the-art approaches and directions for future research.

Authors Francesco Locatello, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, Olivier Bachem

Submitted AAAI 2020

#### Francesco Locatello, Alp Yurtsever, Olivier Fercoq, Volkan Cevher Stochastic Conditional Gradient Method for Composite Convex Minimization NeurIPS 2019

Abstract In this paper, we propose the first practical algorithm to minimize stochastic composite optimization problems over compact convex sets. This template allows for affine constraints and therefore covers stochastic semidefinite programs (SDPs), which are vastly applicable in both machine learning and statistics. In this setup, stochastic algorithms with convergence guarantees are either not known or not tractable. We tackle this general problem and propose a convergent, easy to implement and tractable algorithm. We prove $\mathcal{O}(k^{-1/3})$ convergence rate in expectation on the objective residual and $\mathcal{O}(k^{-5/12})$ in expectation on the feasibility gap. These rates are achieved without increasing the batchsize, which can contain a single sample. We present extensive empirical evidence demonstrating the superiority of our algorithm on a broad range of applications including optimization of stochastic SDPs.

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

Submitted NeurIPS 2019

#### Sjoerd van Steenkiste, Francesco Locatello, Jürgen Schmidhuber, Olivier Bachem Are Disentangled Representations Helpful for Abstract Visual Reasoning? NeurIPS 2019

Abstract A disentangled representation encodes information about the salient factors of variation in the data independently. Although it is often argued that this representational format is useful in learning to solve many real-world up-stream tasks, there is little empirical evidence that supports this claim. In this paper, we conduct a large-scale study that investigates whether disentangled representations are more suitable for abstract reasoning tasks. Using two new tasks similar to Raven's Progressive Matrices, we evaluate the usefulness of the representations learned by 360 state-of-the-art unsupervised disentanglement models. Based on these representations, we train 3600 abstract reasoning models and observe that disentangled representations do in fact lead to better up-stream performance. In particular, they appear to enable quicker learning using fewer samples.

Authors Sjoerd van Steenkiste, Francesco Locatello, Jürgen Schmidhuber, Olivier Bachem

Submitted NeurIPS 2019

#### Francesco Locatello, Gabriele Abbati, Tom Rainforth, Stefan Bauer, Bernhard Schölkopf, Olivier Bachem On the Fairness of Disentangled Representations NeurIPS 2019

Abstract Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an unobserved sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing more than 12600 trained representations of state-of-the-art disentangled models, we observe that various disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.

Authors Francesco Locatello, Gabriele Abbati, Tom Rainforth, Stefan Bauer, Bernhard Schölkopf, Olivier Bachem

Submitted NeurIPS 2019

#### Muhammad Waleed Gondal, Manuel Wüthrich, Đorđe Miladinović, Francesco Locatello, Martin Breidt, Valentin Volchkov, Joel Akpo, Olivier Bachem, Bernhard Schölkopf, Stefan Bauer On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset NeurIPS 2019

Abstract Learning meaningful and compact representations with structurally disentangled semantic aspects is considered to be of key importance in representation learning. Since real-world data is notoriously costly to collect, many recent state-of-the-art disentanglement models have heavily relied on synthetic toy data-sets. In this paper, we propose a novel data-set which consists of over 450'000 images of physical 3D objects with seven factors of variation, such as object color, shape, size and position. In order to be able to control all the factors of variation precisely, we built an experimental platform where the objects are being moved by a robotic arm. In addition, we provide two more datasets which consist of simulations of the experimental setup. These datasets provide for the first time the possibility to systematically investigate how well different disentanglement methods perform on real data in comparison to simulation, and how simulated data can be leveraged to build better representations of the real world.

Authors Muhammad Waleed Gondal, Manuel Wüthrich, Đorđe Miladinović, Francesco Locatello, Martin Breidt, Valentin Volchkov, Joel Akpo, Olivier Bachem, Bernhard Schölkopf, Stefan Bauer

Submitted NeurIPS 2019

#### Luigi Gresele, Paul K Rubenstein, Arash Mehrjou, Francesco Locatello, Bernhard Schölkopf The incomplete rosetta stone problem: Identifiability results for multi-view nonlinear ica UAI 2019

Abstract We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.

Authors Luigi Gresele, Paul K Rubenstein, Arash Mehrjou, Francesco Locatello, Bernhard Schölkopf

Submitted UAI 2019

#### Francesco Locatello, Michael Tschannen, Stefan Bauer, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem Disentangling factors of variation using few labels ICLR 2020

Abstract Learning disentangled representations is considered a cornerstone problem in representation learning. Recently, Locatello et al.(2019) demonstrated that unsupervised disentanglement learning without inductive biases is theoretically impossible and that existing inductive biases and unsupervised methods do not allow to consistently learn disentangled representations. However, in many practical settings, one might have access to a very limited amount of supervision, for example through manual labeling of training examples. In this paper, we investigate the impact of such supervision on state-of-the-art disentanglement methods and perform a large scale study, training over 29000 models under well-defined and reproducible experimental conditions. We first observe that a very limited number of labeled examples (0.01--0.5% of the data set) is sufficient to perform model selection on state-of-the-art unsupervised models. Yet, if one has access to labels for supervised model selection, this raises the natural question of whether they should also be incorporated into the training process. As a case-study, we test the benefit of introducing (very limited) supervision into existing state-of-the-art unsupervised disentanglement methods exploiting both the values of the labels and the ordinal information that can be deduced from them. Overall, we empirically validate that with very little and potentially imprecise supervision it is possible to reliably learn disentangled representations.

Authors Francesco Locatello, Michael Tschannen, Stefan Bauer, Gunnar Rätsch, Bernhard Schölkopf, Olivier Bachem

Submitted ICLR 2020

#### Francesco Locatello, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, Olivier Bachem Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations ICML 2019 - Best Paper Award

Abstract In recent years, the interest in \emph{unsupervised} learning of \emph{disentangled} representations has significantly increased. The key assumption is that real-world data is generated by a few explanatory factors of variation and that these factors can be recovered by unsupervised learning algorithms. A large number of unsupervised learning approaches based on \emph{auto-encoding} and quantitative evaluation metrics of disentanglement have been proposed; yet, the efficacy of the proposed approaches and utility of proposed notions of disentanglement has not been challenged in prior work. In this paper, we provide a sober look on recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than $\num{12000}$ models covering the six most prominent methods, and evaluate them across six disentanglement metrics in a reproducible large-scale experimental study on seven different data sets. On the positive side, we observe that different methods successfully enforce properties encouraged'' by the corresponding losses. On the negative side, we observe that in our study (1) good'' hyperparameters seemingly cannot be identified without access to ground-truth labels, (2) good hyperparameters neither transfer across data sets nor across disentanglement metrics, and (3) that increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. These results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.

Authors Francesco Locatello, Stefan Bauer, Mario Lucic, Gunnar Rätsch, Sylvain Gelly, Bernhard Schölkopf, Olivier Bachem

Submitted ICML 2019 - Best Paper Award

#### Vincent Fortuin, Matthias Hüser, Francesco Locatello, Heiko Strathmann, Gunnar Rätsch SOM-VAE: Interpretable Discrete Representation Learning on Time Series ICLR 2019

Abstract High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most 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 a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation 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 in terms of clustering performance and interpretability 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 on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data.

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

Submitted ICLR 2019

#### 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

#### Francesco Locatello, Gideon Dresdner, Rajiv Khanna, Isabel Valera, Gunnar Rätsch Boosting Black Box Variational Inference NeurIPS 2018 (spotlight)

Abstract Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

Authors Francesco Locatello, Gideon Dresdner, Rajiv Khanna, Isabel Valera, Gunnar Rätsch

Submitted NeurIPS 2018 (spotlight)

#### 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