Foundation Inference Models for Markov Jump Processes

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

Dynamic Review-based Recommenders

Just as user preferences change with time, item reviews also reflect those same preference changes. In a nutshell, if one is to sequentially incorporate review content knowledge into recommender systems, one is naturally led to dynamical models of text. In the present work we leverage the known power of reviews to enhance rating predictions in a way that (i) respects the causality of review generation and (ii) includes, in a bidirectional fashion, the ability of ratings to inform language review models and vice-versa, language representations that help predict ratings end-to-end. Moreover, our representations are time-interval aware and thus yield a continuous-time representation of the dynamics. We provide experiments on real-world datasets and show that our methodology is able to outperform several state-of-the-art models. Source code for all models can be found at [1].

Nonlinear Hawkes Process with Gaussian Process Self Effects

Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes. Efficient approximate Bayesian inference is achieved via data augmentation, and we describe a mean--field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from three different domains and compare it to previously reported results.

Recurrent Point Review Models

Deep neural network models represent the state-of-the-art methodologies for natural language processing. Here we build on top of these methodologies to incorporate temporal information and model how to review data changes with time. Specifically, we use the dynamic representations of recurrent point process models, which encode the history of how business or service reviews are received in time, to generate instantaneous language models with improved prediction capabilities. Simultaneously, our methodologies enhance the predictive power of our point process models by incorporating summarized review content representations. We provide recurrent network and temporal convolution solutions for modeling the review content. We deploy our methodologies in the context of recommender systems, effectively characterizing the change in preference and taste of users as time evolves. Source code is available at [1].

Recurrent Point Processes for Dynamic Review Models

Recent progress in recommender system research has shown the importance of including temporal representations to improve interpretability and performance. Here, we incorporate temporal representations in continuous time via recurrent point process for a dynamical model of reviews. Our goal is to characterize how changes in perception, user interest and seasonal effects affect review text.

Adiabatic Quantum Computing for Binary Clustering

Quantum computing for machine learning attracts increasing attention and recent technological developments suggest that especially adiabatic quantum computing may soon be of practical interest. In this paper, we therefore consider this paradigm and discuss how to adopt it to the problem of binary clustering. Numerical simulations demonstrate the feasibility of our approach and illustrate how systems of qubits adiabatically evolve towards a solution.