Recent studies illustrate how machine learning (ML) can be used to bypass a core challenge of molecular modeling: the tradeoff between accuracy and computational cost. Here, we assess multiple ML approaches for predicting the atomization energy of organic molecules. Our resulting models learn the difference between low-fidelity, B3LYP, and high-accuracy, G4MP2, atomization energies, and predict the G4MP2 atomization energy to 0.005 eV (mean absolute error) for molecules with less than 9 heavy atoms and 0.012 eV for a small set of molecules with between 10 and 14 heavy atoms. Our two best models, which have different accuracy/speed tradeoffs, enable the efficient prediction of G4MP2-level energies for large molecules and are available through a simple web interface.

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present an improvement to training capsule networks with added robustness via non-parametric kernel methods. The representations learned through the capsule network are used to construct covariance kernels for Gaussian processes (GPs). We demonstrate that this approach achieves comparable prediction performance to Capsule Networks while improving robustness to adversarial perturbations and providing a meaningful measure of uncertainty that may aid in the detection of adversarial inputs.

Other authors suggest that specific margin instances Forests (Breiman, 2001) and rotation forests (Rodriguez hold a clue to better generalization (Shen and Li, et al., 2006), create a set of weak classifiers from 2010; Wang et al., 2011, 2012). In this article, we design a base learning algorithm B, which are typically decision algorithms to empirically test whether the state of research trees, then combine the predictions from the classifiers in in the explanation of ensemble performance translates into the form of a weighted vote, to produce an improved prediction better performing algorithms. We do not question the theoretical compared to individual classifiers (Drucker et al., soundness of the generalization error bounds, but 1994; Dietterich, 2000; Breiman, 2001; Maclin and Opitz, simply test whether evidence suggests that better performing 2011). Upper bounds based on the sample margins of the ensemble algorithms can be derived from the practical ensemble provide some explanation on why ensembles perform interpretations of the bounds. In the next section we discuss as well as they do. Schapire et al. (1998) first pointed margins, the generalization error bounds based on the to margins as a key determinant of ensemble performance.

Quantification of the privacy loss associated with a randomised algorithm has become an active area of research and $(\varepsilon,\delta)$-differential privacy has arisen as the standard measure of it. We propose a numerical method for evaluating the parameters of differential privacy for algorithms with continuous one dimensional output. In this way the parameters $\varepsilon$ and $\delta$ can be evaluated, for example, for the subsampled multidimensional Gaussian mechanism which is also the underlying mechanism of differentially private stochastic gradient descent. The proposed method is based on a numerical approximation of an integral formula which gives the exact $(\varepsilon,\delta)$-values. The approximation is carried out by discretising the integral and by evaluating discrete convolutions using a fast Fourier transform algorithm. We give theoretical error bounds which show the convergence of the approximation and guarantee its accuracy to an arbitrary degree. Experimental comparisons with state-of-the-art techniques illustrate the efficacy of the method. Python code for the proposed method can be found in Github (https://github.com/DPBayes/PLD-Accountant/).

A novel resampling framework is proposed to evaluate the robustness and generalization capability of deep learning models with respect to distribution shift. We use Auto Encoder Variational Bayes to find a latent representation of the data, on which a Variational Gaussian Mixture Model is applied to deliberately create distribution shift by dividing the dataset into different clusters. Wasserstein distance is used to characterize the extent of distribution shift between the training and the testing data splits. We compare several conventional Convolutional Neural Network (CNN) architectures as well as Bayesian CNN models for image classification on the Fashion-MNIST dataset to assess their robustness under the deliberately created distribution shift.

Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of the parameter space determined by the Fisher information matrix (FIM), which also corresponds to the local shape of the loss landscape under certain conditions. We analyze deep neural networks with random initialization, which is known to suffer from a pathologically sharp shape of the landscape when the network becomes sufficiently wide. We reveal that batch normalization in the last layer contributes to drastically decreasing such pathological sharpness if the width and sample number satisfy a specific condition. In contrast, it is hard for batch normalization in the middle hidden layers to alleviate pathological sharpness in many settings. We also found that layer normalization cannot alleviate pathological sharpness either. Thus, we can conclude that batch normalization in the last layer significantly contributes to decreasing the sharpness induced by the FIM.

Classifier chains have recently been proposed as an appealing method for tackling the multi-label classification task. In addition to several empirical studies showing its state-of-the-art performance, especially when being used in its ensemble variant, there are also some first results on theoretical properties of classifier chains. Continuing along this line, we analyze the influence of a potential pitfall of the learning process, namely the discrepancy between the feature spaces used in training and testing: While true class labels are used as supplementary attributes for training the binary models along the chain, the same models need to rely on estimations of these labels at prediction time. We elucidate under which circumstances the attribute noise thus created can affect the overall prediction performance. As a result of our findings, we propose two modifications of classifier chains that are meant to overcome this problem. Experimentally, we show that our variants are indeed able to produce better results in cases where the original chaining process is likely to fail.

Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend their application to estimate \emph{structured} approximations such as mixtures of EF distributions. Such approximations can fit complex, multimodal posterior distributions and are generally more accurate than unimodal EF approximations. By using a \emph{minimal conditional-EF} representation of such approximations, we derive simple natural-gradient updates. Our empirical results demonstrate a faster convergence of our natural-gradient method compared to black-box gradient-based methods. Our work expands the scope of natural gradients for Bayesian inference and makes them more widely applicable than before.

Recurrent neural networks (RNNs) are commonly applied to clinical time-series data with the goal of learning patient risk stratification models. Their effectiveness is due, in part, to their use of parameter sharing over time (i.e., cells are repeated hence the name recurrent). We hypothesize, however, that this trait also contributes to the increased difficulty such models have with learning relationships that change over time. Conditional shift, i.e., changes in the relationship between the input X and the output y, arises if the risk factors for the event of interest change over the course of a patient admission. While in theory, RNNs and gated RNNs (e.g., LSTMs) in particular should be capable of learning time-varying relationships, when training data are limited, such models often fail to accurately capture these dynamics. We illustrate the advantages and disadvantages of complete weight sharing (RNNs) by comparing an LSTM with shared parameters to a sequential architecture with time-varying parameters on three clinically-relevant prediction tasks: acute respiratory failure (ARF), shock, and in-hospital mortality. In experiments using synthetic data, we demonstrate how weight sharing in LSTMs leads to worse performance in the presence of conditional shift. To improve upon the dichotomy between complete weight sharing vs. no weight sharing, we propose a novel RNN formulation based on a mixture model in which we relax weight sharing over time. The proposed method outperforms standard LSTMs and other state-of-the-art baselines across all tasks. In settings with limited data, relaxed weight sharing can lead to improved patient risk stratification performance.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density, and reduce the memory required during training by a factor of ten. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid gradient saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.