Rishit Sheth

Syrine Belakaria, Janardhan Rao Doppa, Nicolo Fusi et al.

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 {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative 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.

Yadi Wei, Rishit Sheth, Roni Khardon

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.

Diana Cai, Rishit Sheth, Lester Mackey et al.

Meta-learning leverages related source tasks to learn an initialization that can be quickly fine-tuned to a target task with limited labeled examples. However, many popular meta-learning algorithms, such as model-agnostic meta-learning (MAML), only assume access to the target samples for fine-tuning. In this work, we provide a general framework for meta-learning based on weighting the loss of different source tasks, where the weights are allowed to depend on the target samples. In this general setting, we provide upper bounds on the distance of the weighted empirical risk of the source tasks and expected target risk in terms of an integral probability metric (IPM) and Rademacher complexity, which apply to a number of meta-learning settings including MAML and a weighted MAML variant. We then develop a learning algorithm based on minimizing the error bound with respect to an empirical IPM, including a weighted MAML algorithm, $α$-MAML. Finally, we demonstrate empirically on several regression problems that our weighted meta-learning algorithm is able to find better initializations than uniformly-weighted meta-learning algorithms, such as MAML.

Rishit Sheth, Nicolo Fusi

In this paper we introduce Feature Gradients, 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. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Nicolo Fusi, Rishit Sheth, Huseyn Melih Elibol

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 consisting of data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we tackle this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Using probabilistic matrix factorization techniques and acquisition functions from Bayesian optimization, we exploit experiments performed in hundreds of different datasets to guide the exploration of the space of possible 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.

Rishit Sheth, Roni Khardon

The stochastic variational inference (SVI) paradigm, which combines variational inference, natural gradients, and stochastic updates, was recently proposed for large-scale data analysis in conjugate Bayesian models and demonstrated to be effective in several problems. This paper studies a family of Bayesian latent variable models with two levels of hidden variables but without any conjugacy requirements, making several contributions in this context. The first is observing that SVI, with an improved structured variational approximation, is applicable under more general conditions than previously thought with the only requirement being that the approximating variational distribution be in the same family as the prior. The resulting approach, Monte Carlo Structured SVI (MC-SSVI), significantly extends the scope of SVI, enabling large-scale learning in non-conjugate models. For models with latent Gaussian variables we propose a hybrid algorithm, using both standard and natural gradients, which is shown to improve stability and convergence. Applications in mixed effects models, sparse Gaussian processes, probabilistic matrix factorization and correlated topic models demonstrate the generality of the approach and the advantages of the proposed algorithms.