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  1. Free, publicly-accessible full text available January 1, 2023
  2. Free, publicly-accessible full text available January 1, 2023
  3. In the Proceedings on the 11th International Conference on Probabilistic Graphical Models (PGM), published as part of the PMLR series.
    Free, publicly-accessible full text available January 1, 2023
  4. The paper provides a thorough investigation of Direct Loss Minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square loss showing a significant performance improvement in both cases. The application of DLM in non-conjugate cases is more complex because the logarithm of expectation in the log-loss DLM objective is often intractable and simple sampling leads to biased estimates of gradients. The paper makes two technical contributions to address this. First, a new method using product sampling is proposed, which gives unbiased estimates of gradients (uPS) for the objective function. Second, a theoretical analysis of biased Monte Carlo estimates (bMC) shows that stochastic gradient descent converges despite the biased gradients. Experiments demonstrate empirical success of DLM. A comparison of the sampling methods shows that, while uPS is potentially more sample-efficient, bMC provides a better tradeoff in terms of convergence time and computational efficiency.
  5. We propose that approximate Bayesian algorithms should optimize a new criterion, directly derived from the loss, to calculate their approximate posterior which we refer to as pseudo-posterior. Unlike standard variational inference which optimizes a lower bound on the log marginal likelihood, the new algorithms can be analyzed to provide loss guarantees on the predictions with the pseudo-posterior. Our criterion can be used to derive new sparse Gaussian process algorithms that have error guarantees applicable to various likelihoods.
  6. Bayesian models are established as one of the main successful paradigms for complex problems in machine learning. To handle intractable inference, research in this area has developed new approximation methods that are fast and effective. However, theoretical analysis of the performance of such approximations is not well developed. The paper furthers such analysis by providing bounds on the excess risk of variational inference algorithms and related regularized loss minimization algorithms for a large class of latent variable models with Gaussian latent variables. We strengthen previous results for variational algorithms by showing they are competitive with any point-estimate predictor. Unlike previous work, we also provide bounds on the risk of the \emph{Bayesian} predictor and not just the risk of the Gibbs predictor for the same approximate posterior. The bounds are applied in complex models including sparse Gaussian processes and correlated topic models. Theoretical results are complemented by identifying novel approximations to the Bayesian objective that attempt to minimize the risk directly. An empirical evaluation compares the variational and new algorithms shedding further light on their performance.