arXiv subjects

Amin Nejatbakhsh

Publications and source records attributed to Amin Nejatbakhsh.

8 recordsLinked to original sources

arXiv2025

Modeling Neural Activity with Conditionally Linear Dynamical Systems

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to characterize these dynamics. These models use Gaussian Process (GP) priors to capture the nonlinear dependence of circuit dynamics on task and behavioral variables. Conditioned on these covariates, the data is modeled with linear dynamics. This allows for transparent interpretation and tractable Bayesian inference. We find that CLDS models can perform well even in severely data-limited regimes (e.g. one trial per condition) due to their Bayesian formulation and ability to share statistical power across nearby task conditions. In example applications, we apply CLDS to model thalamic neurons that nonlinearly encode heading direction and to model motor cortical neurons during a cued reaching task.

q-bio.NC↗

arXiv2024

Comparing noisy neural population dynamics using optimal transport distances

Biological and artificial neural systems form high-dimensional neural representations that underpin their computational capabilities. Methods for quantifying geometric similarity in neural representations have become a popular tool for identifying computational principles that are potentially shared across neural systems. These methods generally assume that neural responses are deterministic and static. However, responses of biological systems, and some artificial systems, are noisy and dynamically unfold over time. Furthermore, these characteristics can have substantial influence on a system's computational capabilities. Here, we demonstrate that existing metrics can fail to capture key differences between neural systems with noisy dynamic responses. We then propose a metric for comparing the geometry of noisy neural trajectories, which can be derived as an optimal transport distance between Gaussian processes. We use the metric to compare models of neural responses in different regions of the motor system and to compare the dynamics of latent diffusion models for text-to-image synthesis.

q-bio.NC↗

arXiv2023

Estimating Noise Correlations Across Continuous Conditions With Wishart Processes

The signaling capacity of a neural population depends on the scale and orientation of its covariance across trials. Estimating this "noise" covariance is challenging and is thought to require a large number of stereotyped trials. New approaches are therefore needed to interrogate the structure of neural noise across rich, naturalistic behaviors and sensory experiences, with few trials per condition. Here, we exploit the fact that conditions are smoothly parameterized in many experiments and leverage Wishart process models to pool statistical power from trials in neighboring conditions. We demonstrate that these models perform favorably on experimental data from the mouse visual cortex and monkey motor cortex relative to standard covariance estimators. Moreover, they produce smooth estimates of covariance as a function of stimulus parameters, enabling estimates of noise correlations in entirely unseen conditions as well as continuous estimates of Fisher information--a commonly used measure of signal fidelity. Together, our results suggest that Wishart processes are broadly applicable tools for quantification and uncertainty estimation of noise correlations in trial-limited regimes, paving the way toward understanding the role of noise in complex neural computations and behavior.

stat.AP↗

arXiv2021

Estimating the Unique Information of Continuous Variables

The integration and transfer of information from multiple sources to multiple targets is a core motive of neural systems. The emerging field of partial information decomposition (PID) provides a novel information-theoretic lens into these mechanisms by identifying synergistic, redundant, and unique contributions to the mutual information between one and several variables. While many works have studied aspects of PID for Gaussian and discrete distributions, the case of general continuous distributions is still uncharted territory. In this work we present a method for estimating the unique information in continuous distributions, for the case of one versus two variables. Our method solves the associated optimization problem over the space of distributions with fixed bivariate marginals by combining copula decompositions and techniques developed to optimize variational autoencoders. We obtain excellent agreement with known analytic results for Gaussians, and illustrate the power of our new approach in several brain-inspired neural models. Our method is capable of recovering the effective connectivity of a chaotic network of rate neurons, and uncovers a complex trade-off between redundancy, synergy and unique information in recurrent networks trained to solve a generalized XOR task.

cs.IT↗

arXiv2020

Sinkhorn EM: An Expectation-Maximization algorithm based on entropic optimal transport

We study Sinkhorn EM (sEM), a variant of the expectation maximization (EM) algorithm for mixtures based on entropic optimal transport. sEM differs from the classic EM algorithm in the way responsibilities are computed during the expectation step: rather than assign data points to clusters independently, sEM uses optimal transport to compute responsibilities by incorporating prior information about mixing weights. Like EM, sEM has a natural interpretation as a coordinate ascent procedure, which iteratively constructs and optimizes a lower bound on the log-likelihood. However, we show theoretically and empirically that sEM has better behavior than EM: it possesses better global convergence guarantees and is less prone to getting stuck in bad local optima. We complement these findings with experiments on simulated data as well as in an inference task involving C. elegans neurons and show that sEM learns cell labels significantly better than other approaches.

stat.ML↗

arXiv2019

Temporal Wasserstein non-negative matrix factorization for non-rigid motion segmentation and spatiotemporal deconvolution

Motion segmentation for natural images commonly relies on dense optic flow to yield point trajectories which can be grouped into clusters through various means including spectral clustering or minimum cost multicuts. However, in biological imaging scenarios, such as fluorescence microscopy or calcium imaging, where the signal to noise ratio is compromised and intensity fluctuations occur, optical flow may be difficult to approximate. To this end, we propose an alternative paradigm for motion segmentation based on optimal transport which models the video frames as time-varying mass represented as histograms. Thus, we cast motion segmentation as a temporal non-linear matrix factorization problem with Wasserstein metric loss. The dictionary elements of this factorization yield segmentation of motion into coherent objects while the loading coefficients allow for time-varying intensity signal of the moving objects to be captured. We demonstrate the use of the proposed paradigm on a simulated multielectrode drift scenario, as well as calcium indicating fluorescence microscopy videos of the nematode Caenorhabditis elegans (C. elegans). The latter application has the added utility of extracting neural activity of the animal in freely conducted behavior.

stat.AP↗

arXiv2019

Robust approximate linear regression without correspondence

We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to estimate transformation coefficients using unordered multisets of covariates and responses. Previous theoretical analysis of the problem has been done in a setting where the responses are a complete permutation of the regressed covariates. This paper expands the problem setting by analyzing the cases where only a subset of the responses is a permutation of the regressed covariates in addition to some covariates being outliers. We term this problem \textit{robust regression without correspondence} and provide several algorithms based on random sample consensus for exact and approximate recovery in a noiseless and noisy one-dimensional setting as well as an approximation algorithm for multiple dimensions. The theoretical guarantees of the algorithms are verified in simulated data. We demonstrate an important computational neuroscience application of the proposed framework by demonstrating its effectiveness in a \textit{Caenorhabditis elegans} neuron matching problem where the presence of outliers in both the source and target nematodes is a natural tendency.

stat.ML↗

arXiv2019

Wasserstein total variation filtering

In this paper, we expand upon the theory of trend filtering by introducing the use of the Wasserstein metric as a means to control the amount of spatiotemporal variation in filtered time series data. While trend filtering utilizes regularization to produce signal estimates that are piecewise linear, in the case of $\ell_1$ regularization, or temporally smooth, in the case of $\ell_2$ regularization, it ignores the topology of the spatial distribution of signal. By incorporating the information about the underlying metric space of the pixel layout, the Wasserstein metric is an attractive choice as a regularizer to undercover spatiotemporal trends in time series data. We introduce a globally optimal algorithm for efficiently estimating the filtered signal under a Wasserstein finite differences operator. The efficacy of the proposed algorithm in preserving spatiotemporal trends in time series video is demonstrated in both simulated and fluorescent microscopy videos of the nematode caenorhabditis elegans and compared against standard trend filtering algorithms.

eess.SP↗