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 Bayesian Inference


A Review of Causality for Learning Algorithms in Medical Image Analysis

arXiv.org Artificial Intelligence

Medical image analysis is a vibrant research area that offers doctors and medical practitioners invaluable insight and the ability to accurately diagnose and monitor disease. Machine learning provides an additional boost for this area. However, machine learning for medical image analysis is particularly vulnerable to natural biases like domain shifts that affect algorithmic performance and robustness. In this paper we analyze machine learning for medical image analysis within the framework of Technology Readiness Levels and review how causal analysis methods can fill a gap when creating robust and adaptable medical image analysis algorithms. We review methods using causality in medical imaging AI/ML and find that causal analysis has the potential to mitigate critical problems for clinical translation but that uptake and clinical downstream research has been limited so far.


A Survey of Learning Curves with Bad Behavior: or How More Data Need Not Lead to Better Performance

arXiv.org Artificial Intelligence

Plotting a learner's generalization performance against the training set size results in a so-called learning curve. This tool, providing insight in the behavior of the learner, is also practically valuable for model selection, predicting the effect of more training data, and reducing the computational complexity of training. We set out to make the (ideal) learning curve concept precise and briefly discuss the aforementioned usages of such curves. The larger part of this survey's focus, however, is on learning curves that show that more data does not necessarily leads to better generalization performance. A result that seems surprising to many researchers in the field of artificial intelligence. We point out the significance of these findings and conclude our survey with an overview and discussion of open problems in this area that warrant further theoretical and empirical investigation.


Asymptotic Properties for Bayesian Neural Network in Besov Space

arXiv.org Artificial Intelligence

Neural networks have shown great predictive power when dealing with various unstructured data such as images and natural languages. The Bayesian neural network captures the uncertainty of prediction by putting a prior distribution for the parameter of the model and computing the posterior distribution. In this paper, we show that the Bayesian neural network using spike-and-slab prior has consistency with nearly minimax convergence rate when the true regression function is in the Besov space. Even when the smoothness of the regression function is unknown the same posterior convergence rate holds and thus the spike-and-slab prior is adaptive to the smoothness of the regression function. We also consider the shrinkage prior, which is more feasible than other priors, and show that it has the same convergence rate. In other words, we propose a practical Bayesian neural network with guaranteed asymptotic properties.


Interpretable by Design: Learning Predictors by Composing Interpretable Queries

arXiv.org Artificial Intelligence

There is a growing concern about typically opaque decision-making with high-performance machine learning algorithms. Providing an explanation of the reasoning process in domain-specific terms can be crucial for adoption in risk-sensitive domains such as healthcare. We argue that machine learning algorithms should be interpretable by design and that the language in which these interpretations are expressed should be domain- and task-dependent. Consequently, we base our model's prediction on a family of user-defined and task-specific binary functions of the data, each having a clear interpretation to the end-user. We then minimize the expected number of queries needed for accurate prediction on any given input. As the solution is generally intractable, following prior work, we choose the queries sequentially based on information gain. However, in contrast to previous work, we need not assume the queries are conditionally independent. Instead, we leverage a stochastic generative model (VAE) and an MCMC algorithm (Unadjusted Langevin) to select the most informative query about the input based on previous query-answers. This enables the online determination of a query chain of whatever depth is required to resolve prediction ambiguities. Finally, experiments on vision and NLP tasks demonstrate the efficacy of our approach and its superiority over post-hoc explanations.


Efficient identification of informative features in simulation-based inference

arXiv.org Artificial Intelligence

Simulation-based Bayesian inference (SBI) can be used to estimate the parameters of complex mechanistic models given observed model outputs without requiring access to explicit likelihood evaluations. A prime example for the application of SBI in neuroscience involves estimating the parameters governing the response dynamics of Hodgkin-Huxley (HH) models from electrophysiological measurements, by inferring a posterior over the parameters that is consistent with a set of observations. To this end, many SBI methods employ a set of summary statistics or scientifically interpretable features to estimate a surrogate likelihood or posterior. However, currently, there is no way to identify how much each summary statistic or feature contributes to reducing posterior uncertainty. To address this challenge, one could simply compare the posteriors with and without a given feature included in the inference process. However, for large or nested feature sets, this would necessitate repeatedly estimating the posterior, which is computationally expensive or even prohibitive. Here, we provide a more efficient approach based on the SBI method neural likelihood estimation (NLE): We show that one can marginalize the trained surrogate likelihood post-hoc before inferring the posterior to assess the contribution of a feature. We demonstrate the usefulness of our method by identifying the most important features for inferring parameters of an example HH neuron model. Beyond neuroscience, our method is generally applicable to SBI workflows that rely on data features for inference used in other scientific fields.


Social Interactions for Autonomous Driving: A Review and Perspectives

arXiv.org Artificial Intelligence

No human drives a car in a vacuum; she/he must negotiate with other road users to achieve their goals in social traffic scenes. A rational human driver can interact with other road users in a socially-compatible way through implicit communications to complete their driving tasks smoothly in interaction-intensive, safety-critical environments. This paper aims to review the existing approaches and theories to help understand and rethink the interactions among human drivers toward social autonomous driving. We take this survey to seek the answers to a series of fundamental questions: 1) What is social interaction in road traffic scenes? 2) How to measure and evaluate social interaction? 3) How to model and reveal the process of social interaction? 4) How do human drivers reach an implicit agreement and negotiate smoothly in social interaction? This paper reviews various approaches to modeling and learning the social interactions between human drivers, ranging from optimization theory and graphical models to social force theory and behavioral & cognitive science. We also highlight some new directions, critical challenges, and opening questions for future research.


Personalized Federated Learning with Hidden Information on Personalized Prior

arXiv.org Artificial Intelligence

Federated learning (FL for simplification) is a distributed machine learning technique that utilizes global servers and collaborative clients to achieve privacy-preserving global model training without direct data sharing. However, heterogeneous data problem, as one of FL's main problems, makes it difficult for the global model to perform effectively on each client's local data. Thus, personalized federated learning (PFL for simplification) aims to improve the performance of the model on local data as much as possible. Bayesian learning, where the parameters of the model are seen as random variables with a prior assumption, is a feasible solution to the heterogeneous data problem due to the tendency that the more local data the model use, the more it focuses on the local data, otherwise focuses on the prior. When Bayesian learning is applied to PFL, the global model provides global knowledge as a prior to the local training process. In this paper, we employ Bayesian learning to model PFL by assuming a prior in the scaled exponential family, and therefore propose pFedBreD, a framework to solve the problem we model using Bregman divergence regularization. Empirically, our experiments show that, under the prior assumption of the spherical Gaussian and the first order strategy of mean selection, our proposal significantly outcompetes other PFL algorithms on multiple public benchmarks.


Revisiting Active Sets for Gaussian Process Decoders

arXiv.org Artificial Intelligence

Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled using variational inference and inducing points. In this paper, we revisit active set approximations. We develop a new stochastic estimate of the log-marginal likelihood based on recently discovered links to cross-validation, and we propose a computationally efficient approximation thereof. We demonstrate that the resulting stochastic active sets (SAS) approximation significantly improves the robustness of GP decoder training, while reducing computational cost. The SAS-GP obtains more structure in the latent space, scales to many datapoints, and learns better representations than variational autoencoders, which is rarely the case for GP decoders.


Estimating Regression Predictive Distributions with Sample Networks

arXiv.org Artificial Intelligence

Estimating the uncertainty in deep neural network predictions is crucial for many real-world applications. A common approach to model uncertainty is to choose a parametric distribution and fit the data to it using maximum likelihood estimation. The chosen parametric form can be a poor fit to the data-generating distribution, resulting in unreliable uncertainty estimates. In this work, we propose SampleNet, a flexible and scalable architecture for modeling uncertainty that avoids specifying a parametric form on the output distribution. SampleNets do so by defining an empirical distribution using samples that are learned with the Energy Score and regularized with the Sinkhorn Divergence. SampleNets are shown to be able to well-fit a wide range of distributions and to outperform baselines on large-scale real-world regression tasks.


On learning agent-based models from data

arXiv.org Artificial Intelligence

Agent-Based Models (ABMs) are used in several fields to study the evolution of complex systems from micro-level assumptions. However, ABMs typically can not estimate agent-specific (or "micro") variables: this is a major limitation which prevents ABMs from harnessing micro-level data availability and which greatly limits their predictive power. In this paper, we propose a protocol to learn the latent micro-variables of an ABM from data. The first step of our protocol is to reduce an ABM to a probabilistic model, characterized by a computationally tractable likelihood. This reduction follows two general design principles: balance of stochasticity and data availability, and replacement of unobservable discrete choices with differentiable approximations. Then, our protocol proceeds by maximizing the likelihood of the latent variables via a gradient-based expectation maximization algorithm. We demonstrate our protocol by applying it to an ABM of the housing market, in which agents with different incomes bid higher prices to live in high-income neighborhoods. We demonstrate that the obtained model allows accurate estimates of the latent variables, while preserving the general behavior of the ABM. We also show that our estimates can be used for out-of-sample forecasting. Our protocol can be seen as an alternative to black-box data assimilation methods, that forces the modeler to lay bare the assumptions of the model, to think about the inferential process, and to spot potential identification problems.