More Like this

1. LinCDE: Conditional Density Estimation via Lindsey’s Method

   Gao, Zijun; Hastie, Trevor (January 2022, Journal of machine learning research)

   Conditional density estimation is a fundamental problem in statistics, with scientific and practical applications in biology, economics, finance and environmental studies, to name a few. In this paper, we propose a conditional density estimator based on gradient boosting and Lindsey’s method (LinCDE). LinCDE admits flexible modeling of the density family and can capture distributional characteristics like modality and shape. In particular, when suitably parametrized, LinCDE will produce smooth and non-negative density estimates. Furthermore, like boosted regression trees, LinCDE does automatic feature selection. We demonstrate LinCDE’s efficacy through extensive simulations and three real data examples. 

   more » « less
2. A conditional density estimation partition model using logistic Gaussian processes

   https://doi.org/10.1093/biomet/asz064  

   Payne, R D; Guha, N; Ding, Y; Mallick, B K (December 2019, Biometrika)

   Summary Conditional density estimation seeks to model the distribution of a response variable conditional on covariates. We propose a Bayesian partition model using logistic Gaussian processes to perform conditional density estimation. The partition takes the form of a Voronoi tessellation and is learned from the data using a reversible jump Markov chain Monte Carlo algorithm. The methodology models data in which the density changes sharply throughout the covariate space, and can be used to determine where important changes in the density occur. The Markov chain Monte Carlo algorithm involves a Laplace approximation on the latent variables of the logistic Gaussian process model which marginalizes the parameters in each partition element, allowing an efficient search of the approximate posterior distribution of the tessellation. The method is consistent when the density is piecewise constant in the covariate space or when the density is Lipschitz continuous with respect to the covariates. In simulation and application to wind turbine data, the model successfully estimates the partition structure and conditional distribution. 

   more » « less
3. Diagnostics for conditional density models and Bayesian inference algorithms

   Zhao, David; Dalmasso, Niccolo; Izbicki, Rafael; Lee, Ann B. (January 2021, Proceedings of Machine Learning Research)

   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
4. Your Diffusion Model is Secretly a Zero-Shot Classifier

   Alexander C. Li, Mihir Prabhudesai (September 2023, ICCV)

   The recent wave of large-scale text-to-image diffusion models has dramatically increased our text-based image generation abilities. These models can generate realistic images for a staggering variety of prompts and exhibit impressive compositional generalization abilities. Almost all use cases thus far have solely focused on sampling; however, diffusion models can also provide conditional density estimates, which are useful for tasks beyond image generation. In this paper, we show that the density estimates from large-scale text-to-image diffusion models like Stable Diffusion can be leveraged to perform zero-shot classification without any additional training. Our generative approach to classification, which we call Diffusion Classifier, attains strong results on a variety of benchmarks and outperforms alternative methods of extracting knowledge from diffusion models. Although a gap remains between generative and discriminative approaches on zero-shot recognition tasks, our diffusion-based approach has significantly stronger multimodal compositional reasoning ability than competing discriminative approaches. Finally, we use Diffusion Classifier to extract standard classifiers from class-conditional diffusion models trained on ImageNet. Our models achieve strong classification performance using only weak augmentations and exhibit qualitatively better "effective robustness" to distribution shift. Overall, our results are a step toward using generative over discriminative models for downstream tasks. 

   more » « less
5. Faster Sublinear Algorithms using Conditional Sampling

   Gouleakis, Themistoklis; Tzamos, Christos; Zampetakis, Manolis (January 2017, Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms)

   A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014) has shown that having access to such a conditional sampling oracle requires only polylogarithmic or even constant number of samples to solve distribution testing problems like identity and uniformity. This significantly improves over the standard sampling model where polynomially many samples are necessary. Inspired by these results, we introduce a computational model based on conditional sampling to develop sublinear algorithms with exponentially faster runtimes compared to standard sublinear algorithms. We focus on geometric optimization problems over points in high dimensional Euclidean space. Access to these points is provided via a conditional sampling oracle that takes as input a succinct representation of a subset of the domain and outputs a uniformly random point in that subset. We study two well studied problems: k-means clustering and estimating the weight of the minimum spanning tree. In contrast to prior algorithms for the classic model, our algorithms have time, space and sample complexity that is polynomial in the dimension and polylogarithmic in the number of points. Finally, we comment on the applicability of the model and compare with existing ones like streaming, parallel and distributed computational models. 

   more » « less