Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using any desired f-divergence. We introduce a corresponding optimization algorithm and prove its local convergence property with non-linear dynamical systems theory. Experimental results demonstrate the superiority of f-EBM over contrastive divergence, as well as the benefits of training EBMs using f-divergences other than KL.

Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box approach to dimensionality reduction does not provide sufficient insights. Common data analysis workflows additionally use clustering techniques to identify groups of similar features. This usually leads to a two-stage process, however, it would be desirable to construct a joint modelling framework for simultaneous dimensionality reduction and clustering of features. In this paper, we propose to achieve this through the BasisVAE: a combination of the VAE and a probabilistic clustering prior, which lets us learn a one-hot basis function representation as part of the decoder network. Furthermore, for scenarios where not all features are aligned, we develop an extension to handle translation-invariant basis functions. We show how a collapsed variational inference scheme leads to scalable and efficient inference for BasisVAE, demonstrated on various toy examples as well as on single-cell gene expression data.

In large-scale classification problems, the data set may be faced with frequent updates, e.g., a small ratio of data is added to or removed from the original data set. In this case, incremental learning, which updates an existing classifier by explicitly modeling the data modification, is more efficient than retraining a new classifier from scratch. Conventional incremental learning algorithms try to solve the problem exactly. However, for some tasks, we are only interested in the lower and upper bound for some values relevant to the coefficient vector of the updated classifier without really solving it, e.g., determining whether we should update the classifier or performing some sensitivity analysis tasks. To deal with these such tasks, we propose an algorithm to make rational inferences about the updated classifier with low computational complexity. Specifically, we present a method to calculate tighter bounds of a general linear score for the updated classifier such that it's more accurate to estimate the range of interest than existing papers. The proposed method can be applied to any linear classifiers with differentiable convex L2 regularization loss function. Both theoretical analysis and experiment results show that the proposed approach is superior to existing methods.

Modern meta-learning approaches for image classification rely on increasingly deep networks to achieve state-of-the-art performance, making batch normalization an essential component of meta-learning pipelines. However, the hierarchical nature of the meta-learning setting presents several challenges that can render conventional batch normalization ineffective, giving rise to the need to rethink normalization in this setting. We evaluate a range of approaches to batch normalization for meta-learning scenarios, and develop a novel approach that we call TaskNorm. Experiments on fourteen datasets demonstrate that the choice of batch normalization has a dramatic effect on both classification accuracy and training time for both gradient based and gradient-free meta-learning approaches. Importantly, TaskNorm is found to consistently improve performance. Finally, we provide a set of best practices for normalization that will allow fair comparison of meta-learning algorithms.

The identification of synthetic routes that end with a desired product has been an inherently time-consuming process that is largely dependent on expert knowledge regarding a limited fraction of the entire reaction space. At present, emerging machine-learning technologies are overturning the process of retrosynthetic planning. The objective of this study is to discover synthetic routes backwardly from a given desired molecule to commercially available compounds. The problem is reduced to a combinatorial optimization task with the solution space subject to the combinatorial complexity of all possible pairs of purchasable reactants. We address this issue within the framework of Bayesian inference and computation. The workflow consists of two steps: a deep neural network is trained that forwardly predicts a product of the given reactants with a high level of accuracy, following which this forward model is inverted into the backward one via Bayes' law of conditional probability. Using the backward model, a diverse set of highly probable reaction sequences ending with a given synthetic target is exhaustively explored using a Monte Carlo search algorithm. The Bayesian retrosynthesis algorithm could successfully rediscover 80.3% and 50.0% of known synthetic routes of single-step and two-step reactions within top-10 accuracy, respectively, thereby outperforming state-of-the-art algorithms in terms of the overall accuracy. Remarkably, the Monte Carlo method, which was specifically designed for the presence of diverse multiple routes, often revealed a ranked list of hundreds of reaction routes to the same synthetic target. We investigated the potential applicability of such diverse candidates based on expert knowledge from synthetic organic chemistry.

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Most previous works treat the locations of the inducing variables, i.e. the inducing inputs, as variational hyperparameters, and these are then optimized together with GP covariance hyper-parameters. While some approaches point to the benefits of a Bayesian treatment of GP hyper-parameters, this has been largely overlooked for the inducing inputs. In this work, we show that treating both inducing locations and GP hyper-parameters in a Bayesian way, by inferring their full posterior, further significantly improves performance. Based on stochastic gradient Hamiltonian Monte Carlo, we develop a fully Bayesian approach to scalable GP and deep GP models, and demonstrate its competitive performance through an extensive experimental campaign across several regression and classification problems.

Financial markets exhibit highly non-stationary behaviors, making it difficult to build predictive signals that do not decay too rapidly (see [SCSG13, Con01] for empirical studies of return time series). A standard method for capturing these changes in time series data consists in using a rolling regression, that is, a linear regression model trained on a rolling window and kept as static model during a prediction period. However, the size of historical training data as well as the duration of the prediction period have a direct impact on the performance of the resulting model: using too many training data would result in a model that does not react quickly enough to sudden changes while short training and prediction windows would make the model unstable (see for instance [IJR17]). Online learning algorithms are suited to situations where data arrives sequentially. New information is taken into account by updating the model parameters in a supervised fashion. More precisely, an online learning algorithm repeats the following steps indefinitely: receive a new instance x t, make a prediction ŷ t, receive the correct label y t for the instance and update the model accordingly. In the particular case of regression, online models are also good candidates to handle the non-stationarity inherent in financial time series while keeping a certain memory of what has been learnt from the beginning. The recursive least squares (RLS) algorithm is a well known approach to online linear regression problems (e.g.

We propose Causal Interaction Trees for identifying subgroups of participants that have enhanced treatment effects using observational data. We extend the Classification and Regression Tree algorithm by using splitting criteria that focus on maximizing between-group treatment effect heterogeneity based on subgroup-specific treatment effect estimators to dictate decision-making in the algorithm. We derive properties of three subgroup-specific treatment effect estimators that account for the observational nature of the data -- inverse probability weighting, g-formula and doubly robust estimators. We study the performance of the proposed algorithms using simulations and implement the algorithms in an observational study that evaluates the effectiveness of right heart catheterization on critically ill patients.

As machine learning algorithms are increasingly deployed for high-impact automated decision making, ethical and increasingly also legal standards demand that they treat all individuals fairly, without discrimination based on their age, gender, race or other sensitive traits. In recent years much progress has been made on ensuring fairness and reducing bias in standard machine learning settings. Yet, for network embedding, with applications in vulnerable domains ranging from social network analysis to recommender systems, current options remain limited both in number and performance. We thus propose DeBayes: a conceptually elegant Bayesian method that is capable of learning debiased embeddings by using a biased prior. Our experiments show that these representations can then be used to perform link prediction that is significantly more fair in terms of popular metrics such as demographic parity and equalized opportunity.

Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.