Explains BV Laplacian on half-densities in simple terms.
problem None explicitly stated; focuses on explanation.
method Didactical review of BV Laplacian on half-densities.
result Explains BV Laplacian concept in plain language.
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16 results for “didactical”
Deep neuroevolution, that is evolutionary policy search methods based on deep neural networks, have recently emerged as a competitor to deep reinforcement learning algorithms due to their better parallelization capabilities. However, these methods still suffer from a far worse sample efficiency. In this paper we invest…
Study shows priors are crucial for accurate causal learning from unlabeled data.
problem Improving causal learning from unlabeled data.
method Investigated causal learning using Bayesian methods and analyzed the impact of priors.
result Factorized priors lead to factorized posteriors, aligning with independent causal mechanisms.
This chapter introduces reproducibility in machine learning for medical imaging.
problem Lack of reproducibility in machine learning for medical imaging.
method Distinguishes and defines types of reproducibility, outlines requirements, and discusses utility.
result Discussion on benefits and a plea for a non-dogmatic approach to reproducibility.
Unified reinforcement learning methods using hybrid inference.
problem Combining model-based and model-free reinforcement learning approaches.
method Control as Hybrid Inference (CHI) framework.
result CHI algorithm balances model-based and model-free learning.
Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didacti…
Efficiently updates beliefs with virtual observations.
problem Incremental belief updates in Bayesian models.
method Constructs weighted virtual observations to match posterior.
result Reconstructed posterior matches original posterior closely.
The paper formalizes and analyzes multi-agent Q-learning with value factorization.
problem Understanding and improving the convergence of multi-agent Q-learning with value factorization.
method Formalized a multi-agent fitted Q-iteration framework for analyzing factorized multi-agent Q-learning.
result Multi-agent Q-learning with linear value factorization can converge under certain conditions.
We provide a proof of backpropagation algorithm in matrix notation.
problem The lack of a full induction proof of backpropagation algorithm in matrix notation.
method We provide a full induction proof of the BP algorithm in matrix notation, situating it in the framework of matrix differential calculus.
result We prove the validity of the backpropagation algorithm in inductive form.
In complex systems, many different parts interact in non-obvious ways. Traditional research focuses on a few or a single aspect of the problem so as to analyze it with the tools available. To get a better insight of phenomena that emerge from complex interactions, we need instruments that can analyze simultaneously com…
Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.
problem Processing complex data structures with polyadic relationships.
method Introduction to simplicial complexes and hypergraphs, Fourier analysis, signal denoising, interpolation, embeddings, neural networks.
result Multi-relational operators like the Hodge Laplacian for simplicial complexes and tensor representations for hypergraphs.
Practitioners in medicine, business, political science, and other fields are increasingly aware that decisions should be personalized to each patient, customer, or voter. A given treatment (e.g. a drug or advertisement) should be administered only to those who will respond most positively, and certainly not to those wh…
We give a general treatment of the somewhat unfamiliar operation on manifolds called Connected Sum at Infinity, or CSI for short. A driving ambition has been to make the geometry behind the well definition and basic properties of CSI as clear and elementary as possible. CSI then yields a very natural and elementary pro…
New methods learn DAGs from noisy data, adapting to noise levels.
problem Inferring causal relationships from observational data with noise and confounding.
method Reformulate DAG learning as a continuous optimization problem over adjacency matrices, jointly inferring structure and noise levels.
result Improved robustness to heteroscedasticity and distribution shifts.
New pipeline for causal research in psychology and social sciences.
problem Underuse of causal approaches in psychology and social science.
method Formal specification of theories, reduction of complexity, estimation of causal effects.
result Facilitates scientific inquiry compatible with testing causal theories.
This note presents an elementary proof of Hilbert's 1891 Ansatz of nesting for -sextics, along the line of Riemann's Nachlass 1857 and a simple Harnack-style argument (1876). Our proof seems to have escaped the attention of Hilbert (and all subsequent workers) [but alas turned out to contain a severe gap, cf. Introd…