no code implementations • 14 Feb 2024 • Theodore Papamarkou, Tolga Birdal, Michael Bronstein, Gunnar Carlsson, Justin Curry, Yue Gao, Mustafa Hajij, Roland Kwitt, Pietro Liò, Paolo Di Lorenzo, Vasileios Maroulas, Nina Miolane, Farzana Nasrin, Karthikeyan Natesan Ramamurthy, Bastian Rieck, Simone Scardapane, Michael T. Schaub, Petar Veličković, Bei Wang, Yusu Wang, Guo-Wei Wei, Ghada Zamzmi
Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models.
1 code implementation • 4 Feb 2024 • Mustafa Hajij, Mathilde Papillon, Florian Frantzen, Jens Agerberg, Ibrahem AlJabea, Ruben Ballester, Claudio Battiloro, Guillermo Bernárdez, Tolga Birdal, Aiden Brent, Peter Chin, Sergio Escalera, Simone Fiorellino, Odin Hoff Gardaa, Gurusankar Gopalakrishnan, Devendra Govil, Josef Hoppe, Maneel Reddy Karri, Jude Khouja, Manuel Lecha, Neal Livesay, Jan Meißner, Soham Mukherjee, Alexander Nikitin, Theodore Papamarkou, Jaro Prílepok, Karthikeyan Natesan Ramamurthy, Paul Rosen, Aldo Guzmán-Sáenz, Alessandro Salatiello, Shreyas N. Samaga, Simone Scardapane, Michael T. Schaub, Luca Scofano, Indro Spinelli, Lev Telyatnikov, Quang Truong, Robin Walters, Maosheng Yang, Olga Zaghen, Ghada Zamzmi, Ali Zia, Nina Miolane
We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes.
no code implementations • 2 Feb 2024 • Emanuel Sommer, Lisa Wimmer, Theodore Papamarkou, Ludwig Bothmann, Bernd Bischl, David Rügamer
A major challenge in sample-based inference (SBI) for Bayesian neural networks is the size and structure of the networks' parameter space.
no code implementations • 1 Feb 2024 • Theodore Papamarkou, Maria Skoularidou, Konstantina Palla, Laurence Aitchison, Julyan Arbel, David Dunson, Maurizio Filippone, Vincent Fortuin, Philipp Hennig, Jose Miguel Hernandez Lobato, Aliaksandr Hubin, Alexander Immer, Theofanis Karaletsos, Mohammad Emtiyaz Khan, Agustinus Kristiadi, Yingzhen Li, Stephan Mandt, Christopher Nemeth, Michael A. Osborne, Tim G. J. Rudner, David Rügamer, Yee Whye Teh, Max Welling, Andrew Gordon Wilson, Ruqi Zhang
In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets.
no code implementations • 15 Dec 2023 • Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou, Aldo Guzmán-Sáenz, Tolga Birdal, Michael T. Schaub
In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e. g., to develop a spectral theory.
no code implementations • 19 Oct 2023 • Danny Wood, Theodore Papamarkou, Matt Benatan, Richard Allmendinger
In particular, by adapting permutation feature importance, partial dependence plots, and individual conditional expectation plots, we demonstrate that novel insights into model behaviour may be obtained and that these methods can be used to measure the impact of features on both the entropy of the predictive distribution and the log-likelihood of the ground truth labels under that distribution.
1 code implementation • 26 Sep 2023 • Mathilde Papillon, Mustafa Hajij, Helen Jenne, Johan Mathe, Audun Myers, Theodore Papamarkou, Tolga Birdal, Tamal Dey, Tim Doster, Tegan Emerson, Gurusankar Gopalakrishnan, Devendra Govil, Aldo Guzmán-Sáenz, Henry Kvinge, Neal Livesay, Soham Mukherjee, Shreyas N. Samaga, Karthikeyan Natesan Ramamurthy, Maneel Reddy Karri, Paul Rosen, Sophia Sanborn, Robin Walters, Jens Agerberg, Sadrodin Barikbin, Claudio Battiloro, Gleb Bazhenov, Guillermo Bernardez, Aiden Brent, Sergio Escalera, Simone Fiorellino, Dmitrii Gavrilev, Mohammed Hassanin, Paul Häusner, Odin Hoff Gardaa, Abdelwahed Khamis, Manuel Lecha, German Magai, Tatiana Malygina, Rubén Ballester, Kalyan Nadimpalli, Alexander Nikitin, Abraham Rabinowitz, Alessandro Salatiello, Simone Scardapane, Luca Scofano, Suraj Singh, Jens Sjölund, Pavel Snopov, Indro Spinelli, Lev Telyatnikov, Lucia Testa, Maosheng Yang, Yixiao Yue, Olga Zaghen, Ali Zia, Nina Miolane
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning.
no code implementations • 6 Apr 2023 • Jonas Gregor Wiese, Lisa Wimmer, Theodore Papamarkou, Bernd Bischl, Stephan Günnemann, David Rügamer
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape.
no code implementations • 24 Aug 2022 • Theodore Papamarkou
It is also possible to alleviate vanishing acceptance rates for increasing depth by reducing the proposal variance in deeper layers.
3 code implementations • 1 Jun 2022 • Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou, Nina Miolane, Aldo Guzmán-Sáenz, Karthikeyan Natesan Ramamurthy, Tolga Birdal, Tamal K. Dey, Soham Mukherjee, Shreyas N. Samaga, Neal Livesay, Robin Walters, Paul Rosen, Michael T. Schaub
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations.
no code implementations • 1 Dec 2021 • Theodore Papamarkou, Alexey Lindo
Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis.
no code implementations • 15 Apr 2021 • Theodore Papamarkou, Farzana Nasrin, Austin Lawson, Na Gong, Orlando Rios, Vasileios Maroulas
Topological data analysis (TDA) studies the shape patterns of data.
no code implementations • 6 Mar 2021 • Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou, Vasileios Maroulas, Xuanting Cai
In this work, we propose a method for simplicial complex-level representation learning that embeds a simplicial complex to a universal embedding space in a way that complex-to-complex proximity is preserved.
no code implementations • 28 Sep 2020 • Matthew Baucum, Anahita Khojandi, Theodore Papamarkou
To allow for this, we formulate a special case of recurrent neural networks (RNNs), which we name hidden Markov recurrent neural networks (HMRNNs), and prove that each HMRNN has the same likelihood function as a corresponding discrete-observation HMM.
no code implementations • 18 Aug 2020 • Deborshee Sen, Theodore Papamarkou, David Dunson
We attempt to solve these problems by deploying Markov chain Monte Carlo sampling algorithms (MCMC) for Bayesian inference in ANN models with latent variables.
no code implementations • 4 Jun 2020 • Matt Baucum, Anahita Khojandi, Theodore Papamarkou
Hidden Markov models (HMMs) are commonly used for disease progression modeling when the true patient health state is not fully known.
1 code implementation • 4 May 2020 • Sayar Karmakar, Anirbit Mukherjee, Theodore Papamarkou
In this class of networks, we attempt to learn the network weights in the presence of a malicious oracle doing stochastic, bounded and additive adversarial distortions on the true output during training.
no code implementations • 6 Mar 2020 • Theodore Papamarkou, Hayley Guy, Bryce Kroencke, Jordan Miller, Preston Robinette, Daniel Schultz, Jacob Hinkle, Laura Pullum, Catherine Schuman, Jeremy Renshaw, Stylianos Chatzidakis
The results demonstrate that such a deep learning approach allows to detect the locus of corrosion via smaller tiles, and at the same time to infer with high accuracy whether an image comes from a corroded canister.
no code implementations • 3 Jan 2020 • Devanshu Agrawal, Theodore Papamarkou, Jacob Hinkle
There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width.
1 code implementation • 15 Oct 2019 • Theodore Papamarkou, Jacob Hinkle, M. Todd Young, David Womble
Nevertheless, this paper shows that a non-converged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable posterior predictive distribution of the output of the neural network.
3 code implementations • 29 Aug 2016 • Theodore Papamarkou, Alexey Lindo, Eric B. Ford
This paper analyzes the computational complexity of manifold Langevin Monte Carlo and proposes a geometric adaptive Monte Carlo sampler aimed at balancing the benefits of exploiting local geometry with computational cost to achieve a high effective sample size for a given computational cost.
8 code implementations • 26 Jul 2016 • Jarrett Revels, Miles Lubin, Theodore Papamarkou
We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++.
Mathematical Software