7 research outputs found
Scalable Inference for Neuronal Connectivity from Calcium Imaging
Fluorescent calcium imaging provides a potentially powerful tool for
inferring connectivity in neural circuits with up to thousands of neurons.
However, a key challenge in using calcium imaging for connectivity detection is
that current systems often have a temporal response and frame rate that can be
orders of magnitude slower than the underlying neural spiking process. Bayesian
inference methods based on expectation-maximization (EM) have been proposed to
overcome these limitations, but are often computationally demanding since the
E-step in the EM procedure typically involves state estimation for a
high-dimensional nonlinear dynamical system. In this work, we propose a
computationally fast method for the state estimation based on a hybrid of loopy
belief propagation and approximate message passing (AMP). The key insight is
that a neural system as viewed through calcium imaging can be factorized into
simple scalar dynamical systems for each neuron with linear interconnections
between the neurons. Using the structure, the updates in the proposed hybrid
AMP methodology can be computed by a set of one-dimensional state estimation
procedures and linear transforms with the connectivity matrix. This yields a
computationally scalable method for inferring connectivity of large neural
circuits. Simulations of the method on realistic neural networks demonstrate
good accuracy with computation times that are potentially significantly faster
than current approaches based on Markov Chain Monte Carlo methods.Comment: 14 pages, 3 figure
Rigorous Dynamics and Consistent Estimation in Arbitrarily Conditioned Linear Systems
The problem of estimating a random vector x from noisy linear measurements y
= A x + w with unknown parameters on the distributions of x and w, which must
also be learned, arises in a wide range of statistical learning and linear
inverse problems. We show that a computationally simple iterative
message-passing algorithm can provably obtain asymptotically consistent
estimates in a certain high-dimensional large-system limit (LSL) under very
general parameterizations. Previous message passing techniques have required
i.i.d. sub-Gaussian A matrices and often fail when the matrix is
ill-conditioned. The proposed algorithm, called adaptive vector approximate
message passing (Adaptive VAMP) with auto-tuning, applies to all
right-rotationally random A. Importantly, this class includes matrices with
arbitrarily poor conditioning. We show that the parameter estimates and mean
squared error (MSE) of x in each iteration converge to deterministic limits
that can be precisely predicted by a simple set of state evolution (SE)
equations. In addition, a simple testable condition is provided in which the
MSE matches the Bayes-optimal value predicted by the replica method. The paper
thus provides a computationally simple method with provable guarantees of
optimality and consistency over a large class of linear inverse problems
Estimating Network Structure from Incomplete Event Data
Multivariate Bernoulli autoregressive (BAR) processes model time series of
events in which the likelihood of current events is determined by the times and
locations of past events. These processes can be used to model nonlinear
dynamical systems corresponding to criminal activity, responses of patients to
different medical treatment plans, opinion dynamics across social networks,
epidemic spread, and more. Past work examines this problem under the assumption
that the event data is complete, but in many cases only a fraction of events
are observed. Incomplete observations pose a significant challenge in this
setting because the unobserved events still govern the underlying dynamical
system. In this work, we develop a novel approach to estimating the parameters
of a BAR process in the presence of unobserved events via an unbiased estimator
of the complete data log-likelihood function. We propose a computationally
efficient estimation algorithm which approximates this estimator via Taylor
series truncation and establish theoretical results for both the statistical
error and optimization error of our algorithm. We further justify our approach
by testing our method on both simulated data and a real data set consisting of
crimes recorded by the city of Chicago
A shotgun sampling solution for the common input problem in neural connectivity inference
Inferring connectivity in neuronal networks remains a key challenge in
statistical neuroscience. The `common input' problem presents the major
roadblock: it is difficult to reliably distinguish causal connections between
pairs of observed neurons from correlations induced by common input from
unobserved neurons. Since available recording techniques allow us to sample
from only a small fraction of large networks simultaneously with sufficient
temporal resolution, naive connectivity estimators that neglect these common
input effects are highly biased. This work proposes a `shotgun' experimental
design, in which we observe multiple sub-networks briefly, in a serial manner.
Thus, while the full network cannot be observed simultaneously at any given
time, we may be able to observe most of it during the entire experiment. Using
a generalized linear model for a spiking recurrent neural network, we develop
scalable approximate Bayesian methods to perform network inference given this
type of data, in which only a small fraction of the network is observed in each
time bin. We demonstrate in simulation that, using this method: (1) The shotgun
experimental design can eliminate the biases induced by common input effects.
(2) Networks with thousands of neurons, in which only a small fraction of the
neurons is observed in each time bin, could be quickly and accurately
estimated. (3) Performance can be improved if we exploit prior information
about the probability of having a connection between two neurons, its
dependence on neuronal cell types (e.g., Dale's law), or its dependence on the
distance between neurons
Online neural connectivity estimation with ensemble stimulation
One of the primary goals of systems neuroscience is to relate the structure
of neural circuits to their function, yet patterns of connectivity are
difficult to establish when recording from large populations in behaving
organisms. Many previous approaches have attempted to estimate functional
connectivity between neurons using statistical modeling of observational data,
but these approaches rely heavily on parametric assumptions and are purely
correlational. Recently, however, holographic photostimulation techniques have
made it possible to precisely target selected ensembles of neurons, offering
the possibility of establishing direct causal links. Here, we propose a method
based on noisy group testing that drastically increases the efficiency of this
process in sparse networks. By stimulating small ensembles of neurons, we show
that it is possible to recover binarized network connectivity with a number of
tests that grows only logarithmically with population size under minimal
statistical assumptions. Moreover, we prove that our approach, which reduces to
an efficiently solvable convex optimization problem, can be related to
Variational Bayesian inference on the binary connection weights, and we derive
rigorous bounds on the posterior marginals. This allows us to extend our method
to the streaming setting, where continuously updated posteriors allow for
optional stopping, and we demonstrate the feasibility of inferring connectivity
for networks of up to tens of thousands of neurons online. Finally, we show how
our work can be theoretically linked to compressed sensing approaches, and
compare results for connectivity inference in different settings.Comment: Revised and expanded version of the work that appeared in NeurIPS
202
Context-dependent self-exciting point processes: models, methods, and risk bounds in high dimensions
High-dimensional autoregressive point processes model how current events
trigger or inhibit future events, such as activity by one member of a social
network can affect the future activity of his or her neighbors. While past work
has focused on estimating the underlying network structure based solely on the
times at which events occur on each node of the network, this paper examines
the more nuanced problem of estimating context-dependent networks that reflect
how features associated with an event (such as the content of a social media
post) modulate the strength of influences among nodes. Specifically, we
leverage ideas from compositional time series and regularization methods in
machine learning to conduct network estimation for high-dimensional marked
point processes. Two models and corresponding estimators are considered in
detail: an autoregressive multinomial model suited to categorical marks and a
logistic-normal model suited to marks with mixed membership in different
categories. Importantly, the logistic-normal model leads to a convex negative
log-likelihood objective and captures dependence across categories. We provide
theoretical guarantees for both estimators, which we validate by simulations
and a synthetic data-generating model. We further validate our methods through
two real data examples and demonstrate the advantages and disadvantages of both
approaches
Statistical physics of linear and bilinear inference problems
The recent development of compressed sensing has led to spectacular advances
in the understanding of sparse linear estimation problems as well as in
algorithms to solve them. It has also triggered a new wave of developments in
the related fields of generalized linear and bilinear inference problems, that
have very diverse applications in signal processing and are furthermore a
building block of deep neural networks. These problems have in common that they
combine a linear mixing step and a nonlinear, probabilistic sensing step,
producing indirect measurements of a signal of interest. Such a setting arises
in problems as different as medical or astronomical imaging, clustering, matrix
completion or blind source separation. The aim of this thesis is to propose
efficient algorithms for this class of problems and to perform their
theoretical analysis. To this end, it uses belief propagation, thanks to which
high-dimensional distributions can be sampled efficiently, thus making a
Bayesian approach to inference tractable. The resulting algorithms undergo
phase transitions just as physical systems do. These phase transitions can be
analyzed using the replica method, initially developed in statistical physics
of disordered systems. The analysis reveals phases in which inference is easy,
hard or impossible. These phases correspond to different energy landscapes of
the problem. The main contributions of this thesis can be divided into three
categories. First, the application of known algorithms to concrete problems:
community detection, superposition codes and an innovative imaging system.
Second, a new, efficient message-passing algorithm for a class of problems
called blind sensor calibration. Third, a theoretical analysis of matrix
compressed sensing and of instabilities in Bayesian bilinear inference
algorithms.Comment: Phd thesi