Learning Likelihood Ratios with Neural Network Classifiers
- URL: http://arxiv.org/abs/2305.10500v2
- Date: Mon, 8 Jan 2024 21:09:35 GMT
- Title: Learning Likelihood Ratios with Neural Network Classifiers
- Authors: Shahzar Rizvi, Mariel Pettee, Benjamin Nachman
- Abstract summary: approximations of the likelihood ratio may be computed using clever parametrizations of neural network-based classifiers.
We present a series of empirical studies detailing the performance of several common loss functionals and parametrizations of the classifier output.
- Score: 0.12277343096128711
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The likelihood ratio is a crucial quantity for statistical inference in
science that enables hypothesis testing, construction of confidence intervals,
reweighting of distributions, and more. Many modern scientific applications,
however, make use of data- or simulation-driven models for which computing the
likelihood ratio can be very difficult or even impossible. By applying the
so-called ``likelihood ratio trick,'' approximations of the likelihood ratio
may be computed using clever parametrizations of neural network-based
classifiers. A number of different neural network setups can be defined to
satisfy this procedure, each with varying performance in approximating the
likelihood ratio when using finite training data. We present a series of
empirical studies detailing the performance of several common loss functionals
and parametrizations of the classifier output in approximating the likelihood
ratio of two univariate and multivariate Gaussian distributions as well as
simulated high-energy particle physics datasets.
Related papers
- Structured Radial Basis Function Network: Modelling Diversity for
Multiple Hypotheses Prediction [51.82628081279621]
Multi-modal regression is important in forecasting nonstationary processes or with a complex mixture of distributions.
A Structured Radial Basis Function Network is presented as an ensemble of multiple hypotheses predictors for regression problems.
It is proved that this structured model can efficiently interpolate this tessellation and approximate the multiple hypotheses target distribution.
arXiv Detail & Related papers (2023-09-02T01:27:53Z) - Learning Unnormalized Statistical Models via Compositional Optimization [73.30514599338407]
Noise-contrastive estimation(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise.
In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models.
arXiv Detail & Related papers (2023-06-13T01:18:16Z) - Adaptive Conditional Quantile Neural Processes [9.066817971329899]
Conditional Quantile Neural Processes (CQNPs) are a new member of the neural processes family.
We introduce an extension of quantile regression where the model learns to focus on estimating informative quantiles.
Experiments with real and synthetic datasets demonstrate substantial improvements in predictive performance.
arXiv Detail & Related papers (2023-05-30T06:19:19Z) - How to Combine Variational Bayesian Networks in Federated Learning [0.0]
Federated learning enables multiple data centers to train a central model collaboratively without exposing any confidential data.
deterministic models are capable of performing high prediction accuracy, their lack of calibration and capability to quantify uncertainty is problematic for safety-critical applications.
We study the effects of various aggregation schemes for variational Bayesian neural networks.
arXiv Detail & Related papers (2022-06-22T07:53:12Z) - Nonparametric likelihood-free inference with Jensen-Shannon divergence
for simulator-based models with categorical output [1.4298334143083322]
Likelihood-free inference for simulator-based statistical models has attracted a surge of interest, both in the machine learning and statistics communities.
Here we derive a set of theoretical results to enable estimation, hypothesis testing and construction of confidence intervals for model parameters using computation properties of the Jensen-Shannon- divergence.
Such approximation offers a rapid alternative to more-intensive approaches and can be attractive for diverse applications of simulator-based models.
arXiv Detail & Related papers (2022-05-22T18:00:13Z) - Equivariance Allows Handling Multiple Nuisance Variables When Analyzing
Pooled Neuroimaging Datasets [53.34152466646884]
In this paper, we show how bringing recent results on equivariant representation learning instantiated on structured spaces together with simple use of classical results on causal inference provides an effective practical solution.
We demonstrate how our model allows dealing with more than one nuisance variable under some assumptions and can enable analysis of pooled scientific datasets in scenarios that would otherwise entail removing a large portion of the samples.
arXiv Detail & Related papers (2022-03-29T04:54:06Z) - Amortised Likelihood-free Inference for Expensive Time-series Simulators
with Signatured Ratio Estimation [1.675857332621569]
Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function.
Recent advances in machine learning have introduced novel algorithms for estimating otherwise intractable likelihood functions.
We propose a kernel classifier for sequential data using path signatures based on the recently introduced signature kernel.
arXiv Detail & Related papers (2022-02-23T15:59:34Z) - MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood
Inference from Sampled Trajectories [61.3299263929289]
Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice.
One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio.
We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
arXiv Detail & Related papers (2021-06-03T12:59:16Z) - Multi-Sample Online Learning for Spiking Neural Networks based on
Generalized Expectation Maximization [42.125394498649015]
Spiking Neural Networks (SNNs) capture some of the efficiency of biological brains by processing through binary neural dynamic activations.
This paper proposes to leverage multiple compartments that sample independent spiking signals while sharing synaptic weights.
The key idea is to use these signals to obtain more accurate statistical estimates of the log-likelihood training criterion, as well as of its gradient.
arXiv Detail & Related papers (2021-02-05T16:39:42Z) - Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers.
We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model.
Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
arXiv Detail & Related papers (2020-06-22T21:12:31Z) - Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples.
We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
arXiv Detail & Related papers (2020-05-22T22:30:52Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.