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Predictive models of thermodynamic properties of mixtures are paramount in chemical engineering and chemistry. Classical thermodynamic models are successful in generalizing over (continuous) conditions like temperature and concentration. On the other hand, matrix completion methods (MCMs) from machine learning successfully generalize over (discrete) binary systems; these MCMs can make predictions without any data for a given binary system by implicitly learning commonalities across systems. In the present work, we combine the strengths from both worlds in a hybrid approach. The underlying idea is to predict the pair-interaction energies , as they are used in basically all physical models of liquid mixtures, by an MCM. As an example, we embed an MCM into UNIQUAC, a widely-used physical model for the Gibbs excess energy. We train the resulting hybrid model in a Bayesian machine-learning framework on experimental data for activity coefficients in binary systems of 1146 components from the Dortmund Data Bank. We thereby obtain, for the first time, a complete set of UNIQUAC parameters for all binary systems of these components, which allows us to predict, in principle, activity coefficients at arbitrary temperature and composition for any combination of these components, not only for binary but also for multicomponent systems. The hybrid model even outperforms the best available physical model for predicting activity coefficients, the modified UNIFAC (Dortmund) model. 

We present a generic way to hybridize physical and data-driven methods for predicting physicochemical properties. The approach ‘distills’ the physical method's predictions into a prior model and combines it with sparse experimental data using Bayesian inference. We apply the new approach to predict activity coefficients at infinite dilution and obtain significant improvements compared to the physical and data-driven baselines and established ensemble methods from the machine learning literature. 

We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods [Ballé et al., 2018, Minnen et al., 2018, Lee et al., 2019] build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation of each data point. Drawing on the variational inference perspective on compression [Alemi et al., 2018], we identify three approximation gaps which limit performance in the conventional approach: an amortization gap, a discretization gap, and a marginalization gap. We propose remedies for each of these three limitations based on ideas related to iterative inference, stochastic annealing for discrete optimization, and bits-back coding, resulting in the first application of bits-back coding to lossy compression. In our experiments, which include extensive baseline comparisons and ablation studies, we achieve new state-of-the-art performance on lossy image compression using an established VAE architecture, by changing only the inference method. 

Continuous-time event data are common in applications such as individual behavior data, financial transactions, and medical health records. Modeling such data can be very challenging, in particular for applications with many different types of events, since it requires a model to predict the event types as well as the time of occurrence. Recurrent neural networks that parameterize time-varying intensity functions are the current state-of-the-art for predictive modeling with such data. These models typically assume that all event sequences come from the same data distribution. However, in many applications event sequences are generated by different sources, or users, and their characteristics can be very different. In this paper, we extend the broad class of neural marked point process models to mixtures of latent embeddings, where each mixture component models the characteristic traits of a given user. Our approach relies on augmenting these models with a latent variable that encodes user characteristics, represented by a mixture model over user behavior that is trained via amortized variational inference. We evaluate our methods on four large real-world datasets and demonstrate systematic improvements from our approach over existing work for a variety of predictive metrics such as log-likelihood, next event ranking, and source-of-sequence identification. 

We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike current end-to-end neural compression methods that cater the model to a fixed quantization scheme, our algorithm separates model design and training from quantization. Consequently, our algorithm enables “plug-and-play” compression with variable rate-distortion trade-off, using a single trained model. Our algorithm can be seen as a novel extension of arithmetic coding to the continuous domain, and uses adaptive quantization accuracy based on estimates of posterior uncertainty. Our experimental results demonstrate the importance of taking into account posterior uncertainties, and show that image compression with the proposed algorithm outperforms JPEG over a wide range of bit rates using only a single standard VAE. Further experiments on Bayesian neural word embeddings demonstrate the versatility of the proposed method.