Recently there has been growing interest in learning probabilistic models that admit poly-time inference called tractable probabilistic models from data. Although they generalize poorly as compared to intractable models, they often yield more accurate estimates at prediction time. In this paper, we seek to further explore this trade-off between generalization performance and inference accuracy by proposing a novel, partially tractable representation called cutset Bayesian networks (CBNs). The main idea in CBNs is to partition the variables into two subsets X and Y, learn a (intractable) Bayesian network that represents P(X) and a tractable conditional model that represents P(Y|X). The hope is that the intractable model will help improve generalization while the tractable model, by leveraging Rao-Blackwellised sampling which combines exact inference and sampling, will help improve the prediction accuracy. To compactly model P(Y|X), we introduce a novel tractable representation called conditional cutset networks (CCNs) in which all conditional probability distributions are represented using calibrated classifiers—classifiers which typically yield higher quality probability estimates than conventional classifiers. We show via a rigorous experimental evaluation that CBNs and CCNs yield more accurate posterior estimates than their tractable as well as intractable counterparts.
more » « less- Award ID(s):
- 1652835
- PAR ID:
- 10181781
- Date Published:
- Journal Name:
- Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence
- Page Range / eLocation ID:
- 5751 to 5757
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
Active learning methods, like uncertainty sampling, combined with probabilistic prediction techniques have achieved success in various problems like image classification and text classification. For more complex multivariate prediction tasks, the relationships between labels play an important role in designing structured classifiers with better performance. However, computational time complexity limits prevalent probabilistic methods from effectively supporting active learning. Specifically, while non-probabilistic methods based on structured support vector ma-chines can be tractably applied to predicting cuts and bipartite matchings, conditional random fields are intractable for these structures. We propose an adversarial approach for active learning with structured prediction domains that is tractable for cuts and matching. We evaluate this approach algorithmically in two important structured prediction problems: multi-label classification and object tracking in videos. We demonstrate better accuracy and computational efficiency for our proposed method.more » « less
-
There has been growing interest in the AI community for precise uncertainty quantification. Conditional density models f(y|x), where x represents potentially high-dimensional features, are an integral part of uncertainty quantification in prediction and Bayesian inference. However, it is challenging to assess conditional density estimates and gain insight into modes of failure. While existing diagnostic tools can determine whether an approximated conditional density is compatible overall with a data sample, they lack a principled framework for identifying, locating, and interpreting the nature of statistically significant discrepancies over the entire feature space. In this paper, we present rigorous and easy-to-interpret diagnostics such as (i) the “Local Coverage Test” (LCT), which distinguishes an arbitrarily misspecified model from the true conditional density of the sample, and (ii) “Amortized Local P-P plots” (ALP) which can quickly provide interpretable graphical summaries of distributional differences at any location x in the feature space. Our validation procedures scale to high dimensions and can potentially adapt to any type of data at hand. We demonstrate the effectiveness of LCT and ALP through a simulated experiment and applications to prediction and parameter inference for image data.more » « less
-
Abstract Performance of classifiers is often measured in terms of average accuracy on test data. Despite being a standard measure, average accuracy fails in characterising the fit of the model to the underlying conditional law of labels given the features vector (Y∣X), e.g. due to model misspecification, over fitting, and high-dimensionality. In this paper, we consider the fundamental problem of assessing the goodness-of-fit for a general binary classifier. Our framework does not make any parametric assumption on the conditional law Y∣X and treats that as a black-box oracle model which can be accessed only through queries. We formulate the goodness-of-fit assessment problem as a tolerance hypothesis testing of the form H0:E[Df(Bern(η(X))‖Bern(η^(X)))]≤τ where Df represents an f-divergence function, and η(x), η^(x), respectively, denote the true and an estimate likelihood for a feature vector x admitting a positive label. We propose a novel test, called Goodness-of-fit with Randomisation and Scoring Procedure (GRASP) for testing H0, which works in finite sample settings, no matter the features (distribution-free). We also propose model-X GRASP designed for model-X settings where the joint distribution of the features vector is known. Model-X GRASP uses this distributional information to achieve better power. We evaluate the performance of our tests through extensive numerical experiments.
-
Abstract Preharvest yield estimates can be used for harvest planning, marketing, and prescribing in‐season fertilizer and pesticide applications. One approach that is being widely tested is the use of machine learning (ML) or artificial intelligence (AI) algorithms to estimate yields. However, one barrier to the adoption of this approach is that ML/AI algorithms behave as a black block. An alternative approach is to create an algorithm using Bayesian statistics. In Bayesian statistics, prior information is used to help create the algorithm. However, algorithms based on Bayesian statistics are not often computationally efficient. The objective of the current study was to compare the accuracy and computational efficiency of four Bayesian models that used different assumptions to reduce the execution time. In this paper, the Bayesian multiple linear regression (BLR), Bayesian spatial, Bayesian skewed spatial regression, and the Bayesian nearest neighbor Gaussian process (NNGP) models were compared with ML non‐Bayesian random forest model. In this analysis, soybean (
Glycine max ) yields were the response variable (y ), and spaced‐based blue, green, red, and near‐infrared reflectance that was measured with the PlanetScope satellite were the predictor (x ). Among the models tested, the Bayesian (NNGP;R 2‐testing = 0.485) model, which captures the short‐range correlation, outperformed the (BLR;R 2‐testing = 0.02), Bayesian spatial regression (SRM;R 2‐testing = 0.087), and Bayesian skewed spatial regression (sSRM;R 2‐testing = 0.236) models. However, associated with improved accuracy was an increase in run time from 534 s for the BLR model to 2047 s for the NNGP model. These data show that relatively accurate within‐field yield estimates can be obtained without sacrificing computational efficiency and that the coefficients have biological meaning. However, all Bayesian models had lowerR 2values and higher execution times than the random forest model. -
Abstract Integrative analyses based on statistically relevant associations between genomics and a wealth of intermediary phenotypes (such as imaging) provide vital insights into their clinical relevance in terms of the disease mechanisms. Estimates for uncertainty in the resulting integrative models are however unreliable unless inference accounts for the selection of these associations with accuracy. In this paper, we develop selection-aware Bayesian methods, which (1) counteract the impact of model selection bias through a “selection-aware posterior” in a flexible class of integrative Bayesian models post a selection of promising variables via ℓ1-regularized algorithms; (2) strike an inevitable trade-off between the quality of model selection and inferential power when the same data set is used for both selection and uncertainty estimation. Central to our methodological development, a carefully constructed conditional likelihood function deployed with a reparameterization mapping provides tractable updates when gradient-based Markov chain Monte Carlo (MCMC) sampling is used for estimating uncertainties from the selection-aware posterior. Applying our methods to a radiogenomic analysis, we successfully recover several important gene pathways and estimate uncertainties for their associations with patient survival times.