We revisit the classical analysis of generative vs discriminative models for general exponential families, and high-dimensional settings. Towards this, we develop novel technical machinery, including a notion of separability of general loss functions, which allow us to provide a general framework to obtain l convergence rates for general M-estimators. We use this machinery to analyze l and l2 convergence rates of generative and discriminative models, and provide insights into their nuanced behaviors in high-dimensions. Our results are also applicable to differential parameter estimation, where the quantity of interest is the difference between generative model parameters.

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We prove that the ELBO is bounded, and the EM algorithm contributes to the convergence of ELBO.

Consequently, image datasets depicting these groups have limited capacity to fully represent these demographics and intersectional identities. While we recognize that assigning a bias score based on these limited resources might not be entirely accurate, it is a vital first step in the right direction. Moreover, the bias effect size (Eq 8) may sometimes be unreliable [Meade et al., As described in Sec. 5, we manually compare our best HardNeg Stable Diffusion with vanilla Stable A storefront with'Hello W orld' written on it. This leaves us with 6 categories and 104 prompts:Category Prompts Colours A brown bird and a blue bear. An elephant is behind a tree.

Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing expectations of a discriminative model with respect to a probability distribution defined by an arbitrary generative model has been proven to be hard in general. In fact, the task is intractable even for simple models such as logistic regression and a naive Bayes distribution. In this paper, we identify a pair of generative and discriminative models that enables tractable computation of expectations, as well as moments of any order, of the latter with respect to the former in case of regression. Specifically, we consider expressive probabilistic circuits with certain structural constraints that support tractable probabilistic inference. Moreover, we exploit the tractable computation of high-order moments to derive an algorithm to approximate the expectations for classification scenarios in which exact computations are intractable. Our framework to compute expected predictions allows for handling of missing data during prediction time in a principled and accurate way and enables reasoning about the behavior of discriminative models. We empirically show our algorithm to consistently outperform standard imputation techniques on a variety of datasets. Finally, we illustrate how our framework can be used for exploratory data analysis.