Gašper Tkačik

Manuel Reinhardt, Gašper Tkačik, Pieter Rein ten Wolde

The ability to quantify information transmission is crucial for the analysis and design of natural and engineered systems. The information transmission rate is the fundamental measure for systems with time-varying signals, yet computing it is extremely challenging. In particular, the rate cannot be obtained directly from experimental time-series data without approximations, because of the high dimensionality of the signal trajectory space. Path Weight Sampling (PWS) is a computational technique that makes it possible to obtain the information rate exactly for any stochastic system. However, it requires a mathematical model of the system of interest, be it described by a master equation or a set of differential equations. Here, we present a technique that employs Machine Learning (ML) to develop a generative model from experimental time-series data, which is then combined with PWS to obtain the information rate. We demonstrate the accuracy of this technique, called ML-PWS, by comparing its results on synthetic time-series data generated from a non-linear model against ground-truth results obtained by applying PWS directly to the same model. We illustrate the utility of ML-PWS by applying it to neuronal time-series data.

Bahti Zakirov, Gašper Tkačik

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of real biological datasets are prohibitively laborious, and often impossible. To this end, we introduce a Bayesian meta-learning framework designed to automatically convert raw functional predictions from normative theories into tractable probabilistic models. We employ adaptive deep kernel Gaussian processes, meta-learning a kernel on synthetic data generated from a normative theory. This Theory-Informed Kernel specifies a probabilistic model representing the theory predictions -- usable for both fitting data and rigorously validating the theory. As a demonstration, we apply our framework to the early visual system, using efficient coding as our normative theory. We show improved response prediction accuracy in ex vivo recordings of mouse retinal ganglion cells stimulated by natural scenes compared to conventional data-driven baselines, while providing well-calibrated uncertainty estimates and interpretable representations. Using exact Bayesian model selection, we also show that our informed kernel can accurately infer the degree of theory-match from data, confirming faithful encapsulation of theory structure. This work provides a more general, scalable, and automated approach for integrating theoretical knowledge into data-driven scientific inquiry in neuroscience and beyond.

Jan Humplik, Gašper Tkačik

Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the probability of a state is proportional to an arbitrary positive, strictly decreasing, and twice differentiable function of the state's energy. The precise shape of the nonlinear map from energies to unnormalized probabilities has to be learned from data together with the parameters of the energy function. As a case study we show that the above generalization of a fully visible Boltzmann machine yields an accurate model of neural activity of retinal ganglion cells. We attribute this success to the model's ability to easily capture distributions whose probabilities span a large dynamic range, a possible consequence of latent variables that globally couple the system. Similar features have recently been observed in many datasets, suggesting that our new method has wide applicability.