TY - GEN AB - We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in R^d and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck equation via the method of Evolutionary Γ-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalising the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality. AU - Forkert, Dominik L AU - Maas, Jan AU - Portinale, Lorenzo ID - 10022 T2 - arXiv TI - Evolutionary Γ-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions ER - TY - CONF AB - We study the problem of learning from multiple untrusted data sources, a scenario of increasing practical relevance given the recent emergence of crowdsourcing and collaborative learning paradigms. Specifically, we analyze the situation in which a learning system obtains datasets from multiple sources, some of which might be biased or even adversarially perturbed. It is known that in the single-source case, an adversary with the power to corrupt a fixed fraction of the training data can prevent PAC-learnability, that is, even in the limit of infinitely much training data, no learning system can approach the optimal test error. In this work we show that, surprisingly, the same is not true in the multi-source setting, where the adversary can arbitrarily corrupt a fixed fraction of the data sources. Our main results are a generalization bound that provides finite-sample guarantees for this learning setting, as well as corresponding lower bounds. Besides establishing PAC-learnability our results also show that in a cooperative learning setting sharing data with other parties has provable benefits, even if some participants are malicious. AU - Konstantinov, Nikola H AU - Frantar, Elias AU - Alistarh, Dan-Adrian AU - Lampert, Christoph ID - 8724 SN - 2640-3498 T2 - Proceedings of the 37th International Conference on Machine Learning TI - On the sample complexity of adversarial multi-source PAC learning VL - 119 ER - TY - JOUR AB - Determining the phase diagram of systems consisting of smaller subsystems 'connected' via a tunable coupling is a challenging task relevant for a variety of physical settings. A general question is whether new phases, not present in the uncoupled limit, may arise. We use machine learning and a suitable quasidistance between different points of the phase diagram to study layered spin models, in which the spin variables constituting each of the uncoupled systems (to which we refer as layers) are coupled to each other via an interlayer coupling. In such systems, in general, composite order parameters involving spins of different layers may emerge as a consequence of the interlayer coupling. We focus on the layered Ising and Ashkin–Teller models as a paradigmatic case study, determining their phase diagram via the application of a machine learning algorithm to the Monte Carlo data. Remarkably our technique is able to correctly characterize all the system phases also in the case of hidden order parameters, i.e. order parameters whose expression in terms of the microscopic configurations would require additional preprocessing of the data fed to the algorithm. We correctly retrieve the three known phases of the Ashkin–Teller model with ferromagnetic couplings, including the phase described by a composite order parameter. For the bilayer and trilayer Ising models the phases we find are only the ferromagnetic and the paramagnetic ones. Within the approach we introduce, owing to the construction of convolutional neural networks, naturally suitable for layered image-like data with arbitrary number of layers, no preprocessing of the Monte Carlo data is needed, also with regard to its spatial structure. The physical meaning of our results is discussed and compared with analytical data, where available. Yet, the method can be used without any a priori knowledge of the phases one seeks to find and can be applied to other models and structures. AU - Rzadkowski, Wojciech AU - Defenu, N AU - Chiacchiera, S AU - Trombettoni, A AU - Bighin, Giacomo ID - 8644 IS - 9 JF - New Journal of Physics SN - 13672630 TI - Detecting composite orders in layered models via machine learning VL - 22 ER - TY - JOUR AB - We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model. AU - Mysliwy, Krzysztof AU - Seiringer, Robert ID - 8705 IS - 12 JF - Annales Henri Poincare SN - 1424-0637 TI - Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit VL - 21 ER - TY - JOUR AB - We introduce in this paper AMT2.0, a tool for qualitative and quantitative analysis of hybrid continuous and Boolean signals that combine numerical values and discrete events. The evaluation of the signals is based on rich temporal specifications expressed in extended signal temporal logic, which integrates timed regular expressions within signal temporal logic. The tool features qualitative monitoring (property satisfaction checking), trace diagnostics for explaining and justifying property violations and specification-driven measurement of quantitative features of the signal. We demonstrate the tool functionality on several running examples and case studies, and evaluate its performance. AU - Nickovic, Dejan AU - Lebeltel, Olivier AU - Maler, Oded AU - Ferrere, Thomas AU - Ulus, Dogan ID - 10861 IS - 6 JF - International Journal on Software Tools for Technology Transfer KW - Information Systems KW - Software SN - 1433-2779 TI - AMT 2.0: Qualitative and quantitative trace analysis with extended signal temporal logic VL - 22 ER - TY - JOUR AB - 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. AU - Stark, Stefan G AU - Ficek, Joanna AU - Locatello, Francesco AU - Bonilla, Ximena AU - Chevrier, Stéphane AU - Singer, Franziska AU - Aebersold, Rudolf AU - Al-Quaddoomi, Faisal S AU - Albinus, Jonas AU - Alborelli, Ilaria AU - Andani, Sonali AU - Attinger, Per-Olof AU - Bacac, Marina AU - Baumhoer, Daniel AU - Beck-Schimmer, Beatrice AU - Beerenwinkel, Niko AU - Beisel, Christian AU - Bernasconi, Lara AU - Bertolini, Anne AU - Bodenmiller, Bernd AU - Bonilla, Ximena AU - Casanova, Ruben AU - Chevrier, Stéphane AU - Chicherova, Natalia AU - D'Costa, Maya AU - Danenberg, Esther AU - Davidson, Natalie AU - gan, Monica-Andreea Dră AU - Dummer, Reinhard AU - Engler, Stefanie AU - Erkens, Martin AU - Eschbach, Katja AU - Esposito, Cinzia AU - Fedier, André AU - Ferreira, Pedro AU - Ficek, Joanna AU - Frei, Anja L AU - Frey, Bruno AU - Goetze, Sandra AU - Grob, Linda AU - Gut, Gabriele AU - Günther, Detlef AU - Haberecker, Martina AU - Haeuptle, Pirmin AU - Heinzelmann-Schwarz, Viola AU - Herter, Sylvia AU - Holtackers, Rene AU - Huesser, Tamara AU - Irmisch, Anja AU - Jacob, Francis AU - Jacobs, Andrea AU - Jaeger, Tim M AU - Jahn, Katharina AU - James, Alva R AU - Jermann, Philip M AU - Kahles, André AU - Kahraman, Abdullah AU - Koelzer, Viktor H AU - Kuebler, Werner AU - Kuipers, Jack AU - Kunze, Christian P AU - Kurzeder, Christian AU - Lehmann, Kjong-Van AU - Levesque, Mitchell AU - Lugert, Sebastian AU - Maass, Gerd AU - Manz, Markus AU - Markolin, Philipp AU - Mena, Julien AU - Menzel, Ulrike AU - Metzler, Julian M AU - Miglino, Nicola AU - Milani, Emanuela S AU - Moch, Holger AU - Muenst, Simone AU - Murri, Riccardo AU - Ng, Charlotte KY AU - Nicolet, Stefan AU - Nowak, Marta AU - Pedrioli, Patrick GA AU - Pelkmans, Lucas AU - Piscuoglio, Salvatore AU - Prummer, Michael AU - Ritter, Mathilde AU - Rommel, Christian AU - Rosano-González, María L AU - Rätsch, Gunnar AU - Santacroce, Natascha AU - Castillo, Jacobo Sarabia del AU - Schlenker, Ramona AU - Schwalie, Petra C AU - Schwan, Severin AU - Schär, Tobias AU - Senti, Gabriela AU - Singer, Franziska AU - Sivapatham, Sujana AU - Snijder, Berend AU - Sobottka, Bettina AU - Sreedharan, Vipin T AU - Stark, Stefan AU - Stekhoven, Daniel J AU - Theocharides, Alexandre PA AU - Thomas, Tinu M AU - Tolnay, Markus AU - Tosevski, Vinko AU - Toussaint, Nora C AU - Tuncel, Mustafa A AU - Tusup, Marina AU - Drogen, Audrey Van AU - Vetter, Marcus AU - Vlajnic, Tatjana AU - Weber, Sandra AU - Weber, Walter P AU - Wegmann, Rebekka AU - Weller, Michael AU - Wendt, Fabian AU - Wey, Norbert AU - Wicki, Andreas AU - Wollscheid, Bernd AU - Yu, Shuqing AU - Ziegler, Johanna AU - Zimmermann, Marc AU - Zoche, Martin AU - Zuend, Gregor AU - Rätsch, Gunnar AU - Lehmann, Kjong-Van ID - 14125 IS - Supplement_2 JF - Bioinformatics KW - Computational Mathematics KW - Computational Theory and Mathematics KW - Computer Science Applications KW - Molecular Biology KW - Biochemistry KW - Statistics and Probability TI - SCIM: Universal single-cell matching with unpaired feature sets VL - 36 ER - TY - CONF AB - 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. AU - Locatello, Francesco AU - Bauer, Stefan AU - Lucic, Mario AU - Rätsch, Gunnar AU - Gelly, Sylvain AU - Schölkopf, Bernhard AU - Bachem, Olivier ID - 14186 IS - 9 SN - 9781577358350 T2 - The 34th AAAI Conference on Artificial Intelligence TI - A commentary on the unsupervised learning of disentangled representations VL - 34 ER - TY - CONF AB - 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. AU - Locatello, Francesco AU - Poole, Ben AU - Rätsch, Gunnar AU - Schölkopf, Bernhard AU - Bachem, Olivier AU - Tschannen, Michael ID - 14188 T2 - Proceedings of the 37th International Conference on Machine Learning TI - Weakly-supervised disentanglement without compromises VL - 119 ER - TY - CONF AB - 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. AU - Négiar, Geoffrey AU - Dresdner, Gideon AU - Tsai, Alicia AU - Ghaoui, Laurent El AU - Locatello, Francesco AU - Freund, Robert M. AU - Pedregosa, Fabian ID - 14187 T2 - Proceedings of the 37th International Conference on Machine Learning TI - Stochastic Frank-Wolfe for constrained finite-sum minimization VL - 119 ER - TY - JOUR AB - The idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at 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 over 14000 models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on eight data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, different evaluation metrics do not always agree on what should be considered “disentangled” and exhibit systematic differences in the estimation. Finally, increased disentanglement does not seem to necessarily lead to a decreased sample complexity of learning for downstream tasks. Our 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. AU - Locatello, Francesco AU - Bauer, Stefan AU - Lucic, Mario AU - Rätsch, Gunnar AU - Gelly, Sylvain AU - Schölkopf, Bernhard AU - Bachem, Olivier ID - 14195 JF - Journal of Machine Learning Research TI - A sober look at the unsupervised learning of disentangled representations and their evaluation VL - 21 ER -