Neural spiking activity is generally variable, non-stationary, and exhibits complex dependencies on covariates, such as sensory input or behavior. These dependencies have been proposed to be signatures of specific computations, and so characterizing them with quantitative rigor is critical for understanding neural computations. Approaches based on point processes provide a principled statistical framework for modeling neural spiking activity. However, currently, they only allow the instantaneous mean, but not the instantaneous variability, of responses to depend on covariates. To resolve this limitation, we propose a scalable Bayesian approach generalizing modulated renewal processes using sparse variational Gaussian processes. We leverage pathwise conditioning for computing nonparametric priors over conditional interspike interval distributions and rely on automatic relevance determination to detect lagging interspike interval dependencies beyond renewal order. After systematically validating our method on synthetic data, we apply it to two foundational datasets of animal navigation: head direction cells in freely moving mice and hippocampal place cells in rats running along a linear track. Our model exhibits competitive or better predictive power compared to state-of-the-art baselines, and outperforms them in terms of capturing interspike interval statistics. These results confirm the importance of modeling covariate-dependent spiking variability, and further analyses of our fitted models reveal rich patterns of variability modulation beyond the temporal resolution of flexible count-based approaches.

This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational posterior for each, and make asynchronous streaming updates to a central model. In contrast to previous algorithms, the proposed framework is truly streaming, distributed, asynchronous, learning-rate-free, and truncation-free. The key challenge in developing the framework, arising from fact that BNP models do not impose an inherent ordering on their components, is finding the correspondence between minibatch and central BNP posterior components before performing each update. To address this, the paper develops a combinatorial optimization problem over component correspondences, and provides an efficient solution technique. The paper concludes with an application of the methodology to the DP mixture model, with experimental results demonstrating its practical scalability and performance.

In this work, we present a comprehensive Bayesian posterior analysis of what we term Poisson Hierarchical Indian Buffet Processes, designed for complex random sparse count species sampling models that allow for the sharing of information across and within groups. This analysis covers a potentially infinite number of species and unknown parameters, which, within a Bayesian machine learning context, we are able to learn from as more information is sampled. To achieve our refined results, we employ a range of methodologies drawn from Bayesian latent feature models, random occupancy models, and excursion theory. Despite this complexity, our goal is to make our findings accessible to practitioners, including those who may not be familiar with these areas. To facilitate understanding, we adopt a pseudo-expository style that emphasizes clarity and practical utility. We aim to express our findings in a language that resonates with experts in microbiome and ecological studies, addressing gaps in modeling capabilities while acknowledging that we are not experts ourselves in these fields. This approach encourages the use of our models as basic components of more sophisticated frameworks employed by domain experts, embodying the spirit of the seminal work on the Dirichlet Process. Ultimately, our refined posterior analysis not only yields tractable computational procedures but also enables practical statistical implementation and provides a clear mapping to relevant quantities in microbiome analysis.

Neural spiking activity is generally variable, non-stationary, and exhibits complex dependencies on covariates, such as sensory input or behavior. These dependencies have been proposed to be signatures of specific computations, and so characterizing them with quantitative rigor is critical for understanding neural computations. Approaches based on point processes provide a principled statistical framework for modeling neural spiking activity. However, currently, they only allow the instantaneous mean, but not the instantaneous variability, of responses to depend on covariates. To resolve this limitation, we propose a scalable Bayesian approach generalizing modulated renewal processes using sparse variational Gaussian processes.

The idea of the inheritance of biological processes, such as the developmental process or the life cycle of an organism, has been discussed in the biology literature, but formal mathematical descriptions and plausible data analysis frameworks are lacking. We introduce an extension of the nested Dirichlet Process (nDP) to a multiscale model to aid in understanding the mechanisms by which biological processes are inherited, remain stable, and are modified across generations. To address these issues, we introduce Nested Inheritance Dynamics Algorithm (NIDA). At its primary level, NIDA encompasses all processes unfolding within an individual organism's lifespan. The secondary level delineates the dynamics through which these processes evolve or remain stable over time. This framework allows for the specification of a physical system model at either scale, thus promoting seamless integration with established models of development and heredity.

Skills or low-level policies in reinforcement learning are temporally extended actions that can speed up learning and enable complex behaviours. Recent work in offline reinforcement learning and imitation learning has proposed several techniques for skill discovery from a set of expert trajectories. While these methods are promising, the number K of skills to discover is always a fixed hyperparameter, which requires either prior knowledge about the environment or an additional parameter search to tune it. We first propose a method for offline learning of options (a particular skill framework) exploiting advances in variational inference and continuous relaxations. We then highlight an unexplored connection between Bayesian nonparametrics and offline skill discovery, and show how to obtain a nonparametric version of our model. This version is tractable thanks to a carefully structured approximate posterior with a dynamically-changing number of options, removing the need to specify K. We also show how our nonparametric extension can be applied in other skill frameworks, and empirically demonstrate that our method can outperform state-of-the-art offline skill learning algorithms across a variety of environments. Our code is available at https://github.com/layer6ai-labs/BNPO .

This paper presents a methodology for creating streaming, distributed inference algorithms for Bayesian nonparametric (BNP) models. In the proposed framework, processing nodes receive a sequence of data minibatches, compute a variational posterior for each, and make asynchronous streaming updates to a central model. In contrast to previous algorithms, the proposed framework is truly streaming, distributed, asynchronous, learning-rate-free, and truncation-free. The key challenge in developing the framework, arising from fact that BNP models do not impose an inherent ordering on their components, is finding the correspondence between minibatch and central BNP posterior components before performing each update. To address this, the paper develops a combinatorial optimization problem over component correspondences, and provides an efficient solution technique. The paper concludes with an application of the methodology to the DP mixture model, with experimental results demonstrating its practical scalability and performance.

In this paper, we introduce a method for segmenting time series data using tools from Bayesian nonparametrics. We consider the task of temporal segmentation of a set of time series data into representative stationary segments. We use Gaussian process (GP) priors to impose our knowledge about the characteristics of the underlying stationary segments, and use a nonparametric distribution to partition the sequences into such segments, formulated in terms of a prior distribution on segment length. Given the segmentation, the model can be viewed as a variant of a Gaussian mixture model where the mixture components are described using the covariance function of a GP. We demonstrate the effectiveness of our model on synthetic data as well as on real time-series data of heartbeats where the task is to segment the indicative types of beats and to classify the heartbeat recordings into classes that correspond to healthy and abnormal heart sounds.

Bayesian Nonparametrics is a class of models with a potentially infinite number of parameters. High flexibility and expressive power of this approach enables better data modelling compared to parametric methods. Bayesian Nonparametrics is used in problems where a dimension of interest grows with data, for example, in problems where the number of features is not fixed but allowed to vary as we observe more data. Another example is clustering where the number of clusters is automatically inferred from data. The Statsbot team asked a data scientist, Vadim Smolyakov, to introduce us to Bayesian Nonparametric models.

We propose a Bayesian nonparametric prior for time-varying networks. To each node of the network is associated a positive parameter, modeling the sociability of that node. Sociabilities are assumed to evolve over time, and are modeled via a dynamic point process model. The model is able to (a) capture smooth evolution of the interaction between nodes, allowing edges to appear/disappear over time (b) capture long term evolution of the sociabilities of the nodes (c) and yield sparse graphs, where the number of edges grows subquadratically with the number of nodes. The evolution of the sociabilities is described by a tractable time-varying gamma process. We provide some theoretical insights into the model and apply it to three real world datasets.