Developing new molecular compounds is crucial to address pressing challenges, from health to environmental sustainability. However, exploring the molecular space to discover new molecules is difficult due to the vastness of the space. Here we introduce CoCoGraph, a collaborative and constrained graph diffusion model capable of generating molecules that are guaranteed to be chemically valid. Thanks to the constraints built into the model and to the collaborative mechanism, CoCoGraph outperforms state-of-the-art approaches on standard benchmarks while requiring up to an order of magnitude fewer parameters. Analysis of 36 chemical properties also demonstrates that CoCoGraph generates molecules with distributions more closely matching real molecules than current models. Leveraging the model's efficiency, we created a database of 8.2M million synthetically generated molecules and conducted a Turing-like test with organic chemistry experts to further assess the plausibility of the generated molecules, and potential biases and limitations of CoCoGraph.

Self-driving cars face complex driving situations with a large amount of agents when moving in crowded cities. However, some of the agents are actually not influencing the behavior of the self-driving car. Filtering out unimportant agents would inherently simplify the behavior or motion planning task for the system. The planning system can then focus on fewer agents to find optimal behavior solutions for the ego~agent. This is helpful especially in terms of computational efficiency. In this paper, therefore, the research topic of importance filtering with driving risk models is introduced. We give an overview of state-of-the-art risk models and present newly adapted risk models for filtering. Their capability to filter out surrounding unimportant agents is compared in a large-scale experiment. As it turns out, the novel trajectory distance balances performance, robustness and efficiency well. Based on the results, we can further derive a novel filter architecture with multiple filter steps, for which risk models are recommended for each step, to further improve the robustness. We are confident that this will enable current behavior planning systems to better solve complex situations in everyday driving.

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

Deep neural networks for survival prediction outper-form classical approaches in discrimination, which is the ordering of patients according to their time-of-event. Conversely, classical approaches like the Cox Proportional Hazards model display much better calibration, the correct temporal prediction of events of the underlying distribution. Especially in the medical domain, where it is critical to predict the survival of a single patient, both discrimination and calibration are important performance metrics. Here we present Discrete Calibrated Survival (DCS), a novel deep neural network for discriminated and calibrated survival prediction that outperforms competing survival models in discrimination on three medical datasets, while achieving best calibration among all discrete time models. The enhanced performance of DCS can be attributed to two novel features, the variable temporal output node spacing and the novel loss term that optimizes the use of uncensored and censored patient data. We believe that DCS is an important step towards clinical application of deep-learning-based survival prediction with state-of-the-art discrimination and good calibration.

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided into two types of problem: finding solutions or discovering unknown coefficients of given PDEs with initial and boundary conditions. We introduce three different models: continuous time, discrete time and hybrid models. The given physical information is integrated into Gaussian process model through our designed GP loss functions. Three types of loss function are provided in this paper based on two different approaches to train the standard GP model. The first part of the paper introduces the continuous time model which treats temporal domain the same as spatial domain. The unknown coefficients in given PDEs can be jointly learned with GP hyper-parameters by minimizing the designed loss function. In the discrete time models, we first choose a time discretization scheme to discretize the temporal domain. Then the PAGP model is applied at each time step together with the scheme to approximate PDE solutions at given test points of final time. To discover unknown coefficients in this setting, observations at two specific time are needed and a mixed mean square error function is constructed to obtain the optimal coefficients. In the last part, a novel hybrid model combining the continuous and discrete time models is presented. It merges the flexibility of continuous time model and the accuracy of the discrete time model. The performance of choosing different models with different GP loss functions is also discussed. The effectiveness of the proposed PAGP methods is illustrated in our numerical section.

Finite mixture models have been used for unsupervised learning for some time, and their use within the semi-supervised paradigm is becoming more commonplace. Clickstream data is one of the various emerging data types that demands particular attention because there is a notable paucity of statistical learning approaches currently available. A mixture of first-order continuous time Markov models is introduced for unsupervised and semi-supervised learning of clickstream data. This approach assumes continuous time, which distinguishes it from existing mixture model-based approaches; practically, this allows account to be taken of the amount of time each user spends on each webpage. The approach is evaluated, and compared to the discrete time approach, using simulated and real data.

Event time models predict occurrence times of an event of interest based on known features. Recent work has demonstrated that neural networks achieve state-of-the-art event time predictions in a variety of settings. However, standard event time models suppose that the event occurs, eventually, in all cases. Consequently, no distinction is made between a) the probability of event occurrence, and b) the predicted time of occurrence. This distinction is critical when predicting medical diagnoses, equipment defects, social media posts, and other events that or may not occur, and for which the features affecting a) may be different from those affecting b). In this work, we develop a conditional event time model that distinguishes between these components, implement it as a neural network with a binary stochastic layer representing finite event occurrence, and show how it may be learned from right-censored event times via maximum likelihood estimation. Results demonstrate superior event occurrence and event time predictions on synthetic data, medical events (MIMIC-III), and social media posts (Reddit), comprising 21 total prediction tasks.

Neural Complete is autocomplete based on a generative seq2seq LSTM neural network, trained not only by python code but also on python source code. Ironically, it is trained on files containing keras imports. The result is a neural network trained to help writing neural network code. Rather than completing a word, it will suggest finishing a whole line. It uses information from previous lines to make a suggestion.

We extend chance-constrained path planning with direct method into continuous time. Chance-constrained path planning is a method to obtain the optimal path satisfying a specified risk (or probability of failure) value. Previous work expects trajectories' states as discrete information with respect to time. This discretized encoding makes the conversion from probabilistic path planning to deterministic path planning easy. However, risk guarantees are only produced for the discrete time model. The probability of constraints violation in continuous time could be larger than the discretized risk values. To address this problem, we modified the constraint encoding and risk assessment method. First, we introduce a computationally efficient mean path securing method, which uses fewer binary variables as compared with prior work. Second, we note that the deviation of the actual trajectory from the mean trajectory can be considered as a Brownian motion, for which the reflection principle holds in general. Therefore, we take advantage of the reflection principle to bound the probability of the constraint violation in continuous time. In numerical simulations, we confirmed faster solution generation, and the probability guarantees of the path in the continuous time model, with deterioration in the objective function.