Learning Distributions via Monte-Carlo Marginalization

• URL: http://arxiv.org/abs/2308.06352v1
• Date: Fri, 11 Aug 2023 19:08:06 GMT
• Title: Learning Distributions via Monte-Carlo Marginalization
• Authors: Chenqiu Zhao, Guanfang Dong, Anup Basu
• Abstract summary: We propose a novel method to learn intractable distributions from their samples. The Monte-Carlo Marginalization (MCMarg) is proposed to address this issue. The proposed approach is a powerful tool to learn complex distributions and the entire process is differentiable.
• Score: 9.131712404284876
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We propose a novel method to learn intractable distributions from their samples. The main idea is to use a parametric distribution model, such as a Gaussian Mixture Model (GMM), to approximate intractable distributions by minimizing the KL-divergence. Based on this idea, there are two challenges that need to be addressed. First, the computational complexity of KL-divergence is unacceptable when the dimensions of distributions increases. The Monte-Carlo Marginalization (MCMarg) is proposed to address this issue. The second challenge is the differentiability of the optimization process, since the target distribution is intractable. We handle this problem by using Kernel Density Estimation (KDE). The proposed approach is a powerful tool to learn complex distributions and the entire process is differentiable. Thus, it can be a better substitute of the variational inference in variational auto-encoders (VAE). One strong evidence of the benefit of our method is that the distributions learned by the proposed approach can generate better images even based on a pre-trained VAE's decoder. Based on this point, we devise a distribution learning auto-encoder which is better than VAE under the same network architecture. Experiments on standard dataset and synthetic data demonstrate the efficiency of the proposed approach.

Related papers

• A Stein Gradient Descent Approach for Doubly Intractable Distributions [5.63014864822787]
  We propose a novel Monte Carlo Stein variational gradient descent (MC-SVGD) approach for inference for doubly intractable distributions. The proposed method achieves substantial computational gains over existing algorithms, while providing comparable inferential performance for the posterior distributions.
  arXiv  Detail & Related papers  (2024-10-28T13:42:27Z)
• A Complete Decomposition of KL Error using Refined Information and Mode Interaction Selection [11.994525728378603]
  We revisit the classical formulation of the log-linear model with a focus on higher-order mode interactions. We find that our learned distributions are able to more efficiently use the finite amount of data which is available in practice.
  arXiv  Detail & Related papers  (2024-10-15T18:08:32Z)
• Rejection via Learning Density Ratios [50.91522897152437]
  Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. We propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance. Our framework is tested empirically over clean and noisy datasets.
  arXiv  Detail & Related papers  (2024-05-29T01:32:17Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Dr. FERMI: A Stochastic Distributionally Robust Fair Empirical Risk Minimization Framework [12.734559823650887]
  In the presence of distribution shifts, fair machine learning models may behave unfairly on test data. Existing algorithms require full access to data and cannot be used when small batches are used. This paper proposes the first distributionally robust fairness framework with convergence guarantees that do not require knowledge of the causal graph.
  arXiv  Detail & Related papers  (2023-09-20T23:25:28Z)
• Symmetric Equilibrium Learning of VAEs [56.56929742714685]
  We view variational autoencoders (VAEs) as decoder-encoder pairs, which map distributions in the data space to distributions in the latent space and vice versa. We propose a Nash equilibrium learning approach, which is symmetric with respect to the encoder and decoder and allows learning VAEs in situations where both the data and the latent distributions are accessible only by sampling.
  arXiv  Detail & Related papers  (2023-07-19T10:27:34Z)
• Cramer Type Distances for Learning Gaussian Mixture Models by Gradient Descent [0.0]
  As of today, few known algorithms can fit or learn Gaussian mixture models. We propose a distance function called Sliced Cram'er 2-distance for learning general multivariate GMMs. These features are especially useful for distributional reinforcement learning and Deep Q Networks.
  arXiv  Detail & Related papers  (2023-07-13T13:43:02Z)
• Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity [24.874664446700272]
  This paper studies a new framework that unifies the three approaches and that addresses the two challenges mentioned above. The properties (e.g., consistency and normalities), non-asymptotic properties (e.g., unbiasedness and error bound), and a Monte-Carlo-based solution method of the proposed model are studied.
  arXiv  Detail & Related papers  (2023-01-31T11:33:18Z)
• Distributionally Robust Models with Parametric Likelihood Ratios [123.05074253513935]
  Three simple ideas allow us to train models with DRO using a broader class of parametric likelihood ratios. We find that models trained with the resulting parametric adversaries are consistently more robust to subpopulation shifts when compared to other DRO approaches.
  arXiv  Detail & Related papers  (2022-04-13T12:43:12Z)
• KL Guided Domain Adaptation [88.19298405363452]
  Domain adaptation is an important problem and often needed for real-world applications. A common approach in the domain adaptation literature is to learn a representation of the input that has the same distributions over the source and the target domain. We show that with a probabilistic representation network, the KL term can be estimated efficiently via minibatch samples.
  arXiv  Detail & Related papers  (2021-06-14T22:24:23Z)
• Generative Semantic Hashing Enhanced via Boltzmann Machines [61.688380278649056]
  Existing generative-hashing methods mostly assume a factorized form for the posterior distribution. We propose to employ the distribution of Boltzmann machine as the retrievalal posterior. We show that by effectively modeling correlations among different bits within a hash code, our model can achieve significant performance gains.
  arXiv  Detail & Related papers  (2020-06-16T01:23:39Z)

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.