8,073 research outputs found
Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation
Implicit stochastic models, where the data-generation distribution is
intractable but sampling is possible, are ubiquitous in the natural sciences.
The models typically have free parameters that need to be inferred from data
collected in scientific experiments. A fundamental question is how to design
the experiments so that the collected data are most useful. The field of
Bayesian experimental design advocates that, ideally, we should choose designs
that maximise the mutual information (MI) between the data and the parameters.
For implicit models, however, this approach is severely hampered by the high
computational cost of computing posteriors and maximising MI, in particular
when we have more than a handful of design variables to optimise. In this
paper, we propose a new approach to Bayesian experimental design for implicit
models that leverages recent advances in neural MI estimation to deal with
these issues. We show that training a neural network to maximise a lower bound
on MI allows us to jointly determine the optimal design and the posterior.
Simulation studies illustrate that this gracefully extends Bayesian
experimental design for implicit models to higher design dimensions.Comment: Accepted at the thirty-seventh International Conference on Machine
Learning (ICML) 2020. Camera-ready versio
Bayesian experimental design for implicit models using mutual information
Scientists regularly face the challenging task of designing experiments in such
a way that the collected data is informative and useful. The field of Bayesian
experimental design formalises this task by phrasing it as an optimisation problem. Here, the goal is to maximise a utility function that describes the value of
an experimental design according to the scientific aims of the experiment. The
mutual information, which quantifies the expected information gain about variables of interest, is a principled choice of utility function that has seen extensive
use in literature. However, computing the mutual information is intractable for
all but the most simple computational models of nature. Indeed, as our scientific
theories improve, scientists are increasingly devising models that have intractable
likelihood functions, so-called implicit models. The increased realistic behaviour
of implicit models comes at the cost of severely complicating the Bayesian design
of experiments.
The work presented in this thesis provides several solutions to Bayesian experimental design for implicit models using the mutual information utility function.
Although a desirable quantity, mutual information is generally prohibitively expensive to compute because it involves posterior distributions, which are naturally
intractable for implicit models. Therefore, existing literature has, mostly, either
considered special settings where mutual information can be approximated, or
utilised other simplified utility functions altogether.
First, we present a method of approximating the mutual information using
density ratio estimation techniques, where the only requirement is that we can
sample data from the computational model, which is naturally satisfied for implicit models. This allows us to efficiently estimate the mutual information and
then solve the Bayesian experimental design problem by maximising it by means
of gradient-free optimisation techniques. Following this, we present an extension
that concerns sequential Bayesian experimental design, where the aim is to find
optimal designs and gather data in a sequential manner. We use the density ratios
learned through the aforementioned approach to update our beliefs of the variable of interest at every iteration, which then repeatedly changes the optimisation
landscape. Similar to before, we optimise the sequential mutual information at
every iteration using gradient-free techniques.
Next, we present a method where we construct a lower bound on the mutual
information that is parametrised by a neural network. Neural networks provide great flexibility and, more importantly, allow us to back-propagate from the
lower bound estimate to the experimental designs. We can therefore simultaneously tighten and maximise the mutual information lower bound using stochastic
gradient-ascent. As opposed to previous gradient-free approaches, this results in
greater scalability with respect to the number of experimental design dimensions.
Following this, we provide a general framework that accommodates the use of
(a) several lower bounds with different bias-variance trade-offs and (b) several
important scientific tasks instead of only a single one (as is common in exist ing literature), such as parameter estimation, distinguishing between competing
models and improving future predictions.
Lastly, we present an application of this approach to cognitive science, where
we design behavioural experiments with the aim of estimating parameters of and
distinguishing between cognitive models. We showcase the advantages of our
method by performing real-world experiments with human participants, demonstrating how scientists can use and profit from Bayesian experimental design
methods in practice, even when likelihood functions are intractable
Statistical applications of contrastive learning
The likelihood function plays a crucial role in statistical inference and
experimental design. However, it is computationally intractable for several
important classes of statistical models, including energy-based models and
simulator-based models. Contrastive learning is an intuitive and
computationally feasible alternative to likelihood-based learning. We here
first provide an introduction to contrastive learning and then show how we can
use it to derive methods for diverse statistical problems, namely parameter
estimation for energy-based models, Bayesian inference for simulator-based
models, as well as experimental design.Comment: Accepted to Behaviormetrik
Sequential Bayesian Experimental Design for Implicit Models via Mutual Information
Bayesian experimental design (BED) is a framework that uses statistical
models and decision making under uncertainty to optimise the cost and
performance of a scientific experiment. Sequential BED, as opposed to static
BED, considers the scenario where we can sequentially update our beliefs about
the model parameters through data gathered in the experiment. A class of models
of particular interest for the natural and medical sciences are implicit
models, where the data generating distribution is intractable, but sampling
from it is possible. Even though there has been a lot of work on static BED for
implicit models in the past few years, the notoriously difficult problem of
sequential BED for implicit models has barely been touched upon. We address
this gap in the literature by devising a novel sequential design framework for
parameter estimation that uses the Mutual Information (MI) between model
parameters and simulated data as a utility function to find optimal
experimental designs, which has not been done before for implicit models. Our
approach uses likelihood-free inference by ratio estimation to simultaneously
estimate posterior distributions and the MI. During the sequential BED
procedure we utilise Bayesian optimisation to help us optimise the MI utility.
We find that our framework is efficient for the various implicit models tested,
yielding accurate parameter estimates after only a few iterations
Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation-based Inference
Simulation-based inference (SBI) methods tackle complex scientific models
with challenging inverse problems. However, SBI models often face a significant
hurdle due to their non-differentiable nature, which hampers the use of
gradient-based optimization techniques. Bayesian Optimal Experimental Design
(BOED) is a powerful approach that aims to make the most efficient use of
experimental resources for improved inferences. While stochastic gradient BOED
methods have shown promising results in high-dimensional design problems, they
have mostly neglected the integration of BOED with SBI due to the difficult
non-differentiable property of many SBI simulators. In this work, we establish
a crucial connection between ratio-based SBI inference algorithms and
stochastic gradient-based variational inference by leveraging mutual
information bounds. This connection allows us to extend BOED to SBI
applications, enabling the simultaneous optimization of experimental designs
and amortized inference functions. We demonstrate our approach on a simple
linear model and offer implementation details for practitioners.Comment: Presented at ICML 2023 workshop on Differentiable Everythin
Implicit Deep Adaptive Design: Policy–Based Experimental Design without Likelihoods
We introduce implicit Deep Adaptive Design (iDAD), a new method for
performing adaptive experiments in real-time with implicit models. iDAD
amortizes the cost of Bayesian optimal experimental design (BOED) by learning a
design policy network upfront, which can then be deployed quickly at the time
of the experiment. The iDAD network can be trained on any model which simulates
differentiable samples, unlike previous design policy work that requires a
closed form likelihood and conditionally independent experiments. At
deployment, iDAD allows design decisions to be made in milliseconds, in
contrast to traditional BOED approaches that require heavy computation during
the experiment itself. We illustrate the applicability of iDAD on a number of
experiments, and show that it provides a fast and effective mechanism for
performing adaptive design with implicit models.Comment: 33 pages, 8 figures. Published as a conference paper at NeurIPS 202
Designing Optimal Behavioral Experiments Using Machine Learning
Computational models are powerful tools for understanding human cognition and behavior. They let us express our theories clearly and precisely, and offer predictions that can be subtle and often counter-intuitive. However, this same richness and ability to surprise means our scientific intuitions and traditional tools are ill-suited to designing experiments to test and compare these models. To avoid these pitfalls and realize the full potential of computational modeling, we require tools to design experiments that provide clear answers about what models explain human behavior and the auxiliary assumptions those models must make. Bayesian optimal experimental design (BOED) formalizes the search for optimal experimental designs by identifying experiments that are expected to yield informative data. In this work, we provide a tutorial on leveraging recent advances in BOED and machine learning to find optimal experiments for any kind of model that we can simulate data from, and show how by-products of this procedure allow for quick and straightforward evaluation of models and their parameters against real experimental data. As a case study, we consider theories of how people balance exploration and exploitation in multi-armed bandit decision-making tasks. We validate the presented approach using simulations and a real-world experiment. As compared to experimental designs commonly used in the literature, we show that our optimal designs more efficiently determine which of a set of models best account for individual human behavior, and more efficiently characterize behavior given a preferred model. At the same time, formalizing a scientific question such that it can be adequately addressed with BOED can be challenging and we discuss several potential caveats and pitfalls that practitioners should be aware of. We provide code and tutorial notebooks to replicate all analyses
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