The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as Budget-Aware Planning for Iterative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.

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.

In this paper, we introduce Differentiable Feature Selection, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e. in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N. This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Our algorithm utilizes higher-order correlations between features and targets for both the N>D and N Cite this Paper BibTeX @InProceedings{pmlr-v108-sheth20a, title = {Differentiable Feature Selection by Discrete Relaxation}, author = {Sheth, Rishit and Fusi, Nicol\'o}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {1564--1572}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/sheth20a/sheth20a.pdf}, url = {https://proceedings.mlr.press/v108/sheth20a.html}, abstract = {In this paper, we introduce Differentiable Feature Selection, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e. in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N. This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Our algorithm utilizes higher-order correlations between features and targets for both the N>D and N Copy to Clipboard Download Endnote %0 Conference Paper %T Differentiable Feature Selection by Discrete Relaxation %A Rishit Sheth %A Nicoló Fusi %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-sheth20a %I PMLR %P 1564--1572 %U https://proceedings.mlr.press/v108/sheth20a.html %V 108 %X In this paper, we introduce Differentiable Feature Selection, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e. in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N. This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Our algorithm utilizes higher-order correlations between features and targets for both the N>D and N Copy to Clipboard Download APA Sheth, R. & Fusi, N.. (2020). Differentiable Feature Selection by Discrete Relaxation. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:1564-1572 Available from https://proceedings.mlr.press/v108/sheth20a.html. Copy to Clipboard Download Related Material Download PDF This site last compiled Sun, 05 Jul 2026 14:49:58 +0000 Github Account Copyright © The authors and PMLR 2026. MLResearchPress

In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines, which can include different data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we propose to solve this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Specifically, we use a probabilistic matrix factorization model to transfer knowledge across experiments performed in hundreds of different datasets and use an acquisition function to guide the exploration of the space of possible ML pipelines. In our experiments, we show that our approach quickly identifies high-performing pipelines across a wide range of datasets, significantly outperforming the current state-of-the-art.

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.

Latent Gaussian Models (LGM) provide a rich modeling framework with general inference procedures. The variational approximation offers an effective solution for such models and has attracted a significant amount of interest. Recent work proposed a fixed-point (FP) update procedure to optimize the covariance matrix in the variational solution and demonstrated its efficacy in specific models. The paper makes three contributions. First, it shows that the same approach can be used more generally in extensions of LGM. Second, it provides an analysis identifying conditions for the convergence of the FP method. Third, it provides an extensive experimental evaluation in Gaussian processes, sparse Gaussian processes, and generalized linear models, with several non-conjugate observation likelihoods, showing wide applicability of the FP method and a significant advantage over gradient based optimization.

Gaussian processes (GP) provide an attractive machine learning model due to their non-parametric form, their flexibility to capture many types of observation data, and their generic inference procedures. Sparse GP inference algorithms address the cubic complexity of GPs by focusing on a small set of pseudo-samples. To date, such approaches have focused on the simple case of Gaussian observation likelihoods. This paper develops a variational sparse solution for GPs under general likelihoods by providing a new characterization of the gradients required for inference in terms of individual observation likelihood terms. In addition, we propose a simple new approach for optimizing the sparse variational approximation using a fixed point computation. We demonstrate experimentally that the fixed point operator acts as a contraction in many cases and therefore leads to fast convergence. An experimental evaluation for count regression, classification, and ordinal regression illustrates the generality and advantages of the new approach.