arXiv subjects

Anirvan M. Sengupta

Publications and source records attributed to Anirvan M. Sengupta.

At least 37 records · Page 2Linked to original sources

arXiv2021

Neural circuits for dynamics-based segmentation of time series

The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the waveform. Therefore, one problem faced by the brain is to segment time series based on underlying dynamics. We present two algorithms for performing this segmentation task that are biologically plausible, which we define as acting in a streaming setting and all learning rules being local. One algorithm is model-based and can be derived from an optimization problem involving a mixture of autoregressive processes. This algorithm relies on feedback in the form of a prediction error, and can also be used for forecasting future samples. In some brain regions, such as the retina, the feedback connections necessary to use the prediction error for learning are absent. For this case, we propose a second, model-free algorithm that uses a running estimate of the autocorrelation structure of the signal to perform the segmentation. We show that both algorithms do well when tasked with segmenting signals drawn from autoregressive models with piecewise-constant parameters. In particular, the segmentation accuracy is similar to that obtained from oracle-like methods in which the ground-truth parameters of the autoregressive models are known. We also test our methods on datasets generated by alternating snippets of voice recordings. We provide implementations of our algorithms at https://github.com/ttesileanu/bio-time-series.

q-bio.NC↗

arXiv2021

Informationally complete POVM-based shadow tomography

Recently introduced shadow tomography protocols use classical shadows of quantum states to predict many target functions of an unknown quantum state. Unlike full quantum state tomography, shadow tomography does not insist on accurate recovery of the density matrix for high rank mixed states. Yet, such a protocol makes multiple accurate predictions with high confidence, based on a moderate number of quantum measurements. One particular influential algorithm, proposed by Huang, Kueng, and Preskill arXiv:2002.08953, requires additional circuits for performing certain random unitary transformations. In this paper, we avoid these transformations but employ an arbitrary informationally complete POVM and show that such a procedure can compute k-bit correlation functions for quantum states reliably. We also show that, for this application, we do not need the median of means procedure of Huang et al. Finally, we discuss the contrast between the computation of correlation functions and fidelity of reconstruction of low rank density matrices.

quant-ph↗

arXiv2021

A biologically plausible neural network for multi-channel Canonical Correlation Analysis

Cortical pyramidal neurons receive inputs from multiple distinct neural populations and integrate these inputs in separate dendritic compartments. We explore the possibility that cortical microcircuits implement Canonical Correlation Analysis (CCA), an unsupervised learning method that projects the inputs onto a common subspace so as to maximize the correlations between the projections. To this end, we seek a multi-channel CCA algorithm that can be implemented in a biologically plausible neural network. For biological plausibility, we require that the network operates in the online setting and its synaptic update rules are local. Starting from a novel CCA objective function, we derive an online optimization algorithm whose optimization steps can be implemented in a single-layer neural network with multi-compartmental neurons and local non-Hebbian learning rules. We also derive an extension of our online CCA algorithm with adaptive output rank and output whitening. Interestingly, the extension maps onto a neural network whose neural architecture and synaptic updates resemble neural circuitry and synaptic plasticity observed experimentally in cortical pyramidal neurons.

q-bio.NC↗

arXiv2021

A Similarity-preserving Neural Network Trained on Transformed Images Recapitulates Salient Features of the Fly Motion Detection Circuit

Learning to detect content-independent transformations from data is one of the central problems in biological and artificial intelligence. An example of such problem is unsupervised learning of a visual motion detector from pairs of consecutive video frames. Rao and Ruderman formulated this problem in terms of learning infinitesimal transformation operators (Lie group generators) via minimizing image reconstruction error. Unfortunately, it is difficult to map their model onto a biologically plausible neural network (NN) with local learning rules. Here we propose a biologically plausible model of motion detection. We also adopt the transformation-operator approach but, instead of reconstruction-error minimization, start with a similarity-preserving objective function. An online algorithm that optimizes such an objective function naturally maps onto an NN with biologically plausible learning rules. The trained NN recapitulates major features of the well-studied motion detector in the fly. In particular, it is consistent with the experimental observation that local motion detectors combine information from at least three adjacent pixels, something that contradicts the celebrated Hassenstein-Reichardt model.

cs.NE↗

arXiv2020

A biologically plausible neural network for local supervision in cortical microcircuits

The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer network, we derive an algorithm for training a neural network which avoids this problem by not requiring explicit error computation and backpropagation. Furthermore, our algorithm maps onto a neural network that bears a remarkable resemblance to the connectivity structure and learning rules of the cortex. We find that our algorithm empirically performs comparably to backprop on a number of datasets.

cs.NE↗

arXiv2020

A simple normative network approximates local non-Hebbian learning in the cortex

To guide behavior, the brain extracts relevant features from high-dimensional data streamed by sensory organs. Neuroscience experiments demonstrate that the processing of sensory inputs by cortical neurons is modulated by instructive signals which provide context and task-relevant information. Here, adopting a normative approach, we model these instructive signals as supervisory inputs guiding the projection of the feedforward data. Mathematically, we start with a family of Reduced-Rank Regression (RRR) objective functions which include Reduced Rank (minimum) Mean Square Error (RRMSE) and Canonical Correlation Analysis (CCA), and derive novel offline and online optimization algorithms, which we call Bio-RRR. The online algorithms can be implemented by neural networks whose synaptic learning rules resemble calcium plateau potential dependent plasticity observed in the cortex. We detail how, in our model, the calcium plateau potential can be interpreted as a backpropagating error signal. We demonstrate that, despite relying exclusively on biologically plausible local learning rules, our algorithms perform competitively with existing implementations of RRMSE and CCA.

q-bio.NC↗

arXiv2019

Critical Behavior and Universality Classes for an Algorithmic Phase Transition in Sparse Reconstruction

Recovery of an $N$-dimensional, $K$-sparse solution $\mathbf{x}$ from an $M$-dimensional vector of measurements $\mathbf{y}$ for multivariate linear regression can be accomplished by minimizing a suitably penalized least-mean-square cost $||\mathbf{y}-\mathbf{H} \mathbf{x}||_2^2+λV(\mathbf{x})$. Here $\mathbf{H}$ is a known matrix and $V(\mathbf{x})$ is an algorithm-dependent sparsity-inducing penalty. For `random' $\mathbf{H}$, in the limit $λ\rightarrow 0$ and $M,N,K\rightarrow \infty$, keeping $ρ=K/N$ and $α=M/N$ fixed, exact recovery is possible for $α$ past a critical value $α_c = α(ρ)$. Assuming $\mathbf{x}$ has iid entries, the critical curve exhibits some universality, in that its shape does not depend on the distribution of $\mathbf{x}$. However, the algorithmic phase transition occurring at $α=α_c$ and associated universality classes remain ill-understood from a statistical physics perspective, i.e. in terms of scaling exponents near the critical curve. In this article, we analyze the mean-field equations for two algorithms, Basis Pursuit ($V(\mathbf{x})=||\mathbf{x}||_{1} $) and Elastic Net ($V(\mathbf{x})= ||\mathbf{x}||_{1} + \tfrac{g}{2} ||\mathbf{x}||_{2}^2$) and show that they belong to different universality classes in the sense of scaling exponents, with Mean Squared Error (MSE) of the recovered vector scaling as $λ^\frac{4}{3}$ and $λ$ respectively, for small $λ$ on the critical line. In the presence of additive noise, we find that, when $α>α_c$, MSE is minimized at a non-zero value for $λ$, whereas at $α=α_c$, MSE always increases with $λ$.

cs.IT↗

arXiv2019

A Neural Network for Semi-Supervised Learning on Manifolds

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds without using an explicit graph representation. Our algorithm uses channels that represent localities on the manifold such that correlations between channels represent manifold structure. The proposed neural network has two layers. The first layer learns to build a representation of low-dimensional manifolds in the input data as proposed recently in [8]. The second learns to classify data using both occasional supervision and similarity of the manifold representation of the data. The channel carrying label information for the second layer is assumed to be "silent" most of the time. Learning in both layers is Hebbian, making our network design biologically plausible. We experimentally demonstrate the effect of semi-supervised learning on non-trivial manifolds.

cs.LG↗

arXiv2018

Clustering is semidefinitely not that hard: Nonnegative SDP for manifold disentangling

In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which yields the same solution as the non-convex original formulation for well segregated datasets. We report an unexpected finding: when data contains (greater than zero-dimensional) manifolds, the SDP solution captures such geometrical structures. Unlike traditional manifold embedding techniques, our approach does not rely on manually defining a kernel but rather enforces locality via a nonnegativity constraint. We thus call our approach NOnnegative MAnifold Disentangling, or NOMAD. To build an intuitive understanding of its manifold learning capabilities, we develop a theoretical analysis of NOMAD on idealized datasets. While NOMAD is convex and the globally optimal solution can be found by generic SDP solvers with polynomial time complexity, they are too slow for modern datasets. To address this problem, we analyze a non-convex heuristic and present a new, convex and yet efficient, algorithm, based on the conditional gradient method. Our results render NOMAD a versatile, understandable, and powerful tool for manifold learning.

cs.LG↗

arXiv2015

The cavity method for analysis of large-scale penalized regression

Penalized regression methods aim to retrieve reliable predictors among a large set of putative ones from a limited amount of measurements. In particular, penalized regression with singular penalty functions is important for sparse reconstruction algorithms. For large-scale problems, these algorithms exhibit sharp phase transition boundaries where sparse retrieval breaks down. Large optimization problems associated with sparse reconstruction have been analyzed in the literature by setting up corresponding statistical mechanical models at a finite temperature. Using replica method for mean field approximation, and subsequently taking a zero temperature limit, this approach reproduces the algorithmic phase transition boundaries. Unfortunately, the replica trick and the non-trivial zero temperature limit obscure the underlying reasons for the failure of a sparse reconstruction algorithm, and of penalized regression methods, in general. In this paper, we employ the ``cavity method'' to give an alternative derivation of the mean field equations, working directly in the zero-temperature limit. This derivation provides insight into the origin of the different terms in the self-consistency conditions. The cavity method naturally involves a quantity, the average local susceptibility, whose behavior distinguishes different phases in this system. This susceptibility can be generalized for analysis of a broader class of sparse reconstruction algorithms.

cs.IT↗

arXiv2013

The role of multiple marks in epigenetic silencing and the emergence of a stable bivalent chromatin state

We introduce and analyze a minimal model of epigenetic silencing in budding yeast, built upon known biomolecular interactions in the system. Doing so, we identify the epigenetic marks essential for the bistability of epigenetic states. The model explicitly incorporates two key chromatin marks, namely H4K16 acetylation and H3K79 methylation, and explores whether the presence of multiple marks lead to a qualitatively different systems behavior. We find that having both modifications is important for the robustness of epigenetic silencing. Besides the silenced and transcriptionally active fate of chromatin, our model leads to a novel state with bivalent (i.e., both active and silencing) marks under certain perturbations (knock-out mutations, inhibition or enhancement of enzymatic activity). The bivalent state appears under several perturbations and is shown to result in patchy silencing. We also show that the titration effect, owing to a limited supply of silencing proteins, can result in counter-intuitive responses. The design principles of the silencing system is systematically investigated and disparate experimental observations are assessed within a single theoretical framework. Specifically, we discuss the behavior of Sir protein recruitment, spreading and stability of silenced regions in commonly-studied mutants (e.g., sas2, dot1) illuminating the controversial role of Dot1 in the systems biology of yeast silencing.

q-bio.MN↗

arXiv2013

Titration and hysteresis in epigenetic chromatin silencing

Epigenetic mechanisms of silencing via heritable chromatin modifications play a major role in gene regulation and cell fate specification. We consider a model of epigenetic chromatin silencing in budding yeast and study the bifurcation diagram and characterize the bistable and the monostable regimes. The main focus of this paper is to examine how the perturbations altering the activity of histone modifying enzymes affect the epigenetic states. We analyze the implications of having the total number of silencing proteins given by the sum of proteins bound to the nucleosomes and the ones available in the ambient to be constant. This constraint couples different regions of chromatin through the shared reservoir of ambient silencing proteins. We show that the response of the system to perturbations depends dramatically on the titration effect caused by the above constraint. In particular, for a certain range of overall abundance of silencing proteins, the hysteresis loop changes qualitatively with certain jump replaced by continuous merger of different states. In addition, we find a nonmonotonic dependence of gene expression on the rate of histone deacetylation activity of Sir2. We discuss how these qualitative predictions of our model could be compared with experimental studies of the yeast system under anti-silencing drugs.

q-bio.MN↗

arXiv2012

What does the Allen Gene Expression Atlas tell us about mouse brain evolution?

We use the Allen Gene Expression Atlas (AGEA) and the OMA ortholog dataset to investigate the evolution of mouse-brain neuroanatomy from the standpoint of the molecular evolution of brain-specific genes. For each such gene, using the phylogenetic tree for all fully sequenced species and the presence of orthologs of the gene in these species, we construct and assign a discrete measure of evolutionary age. The gene expression profile of all gene of similar age, relative to the average gene expression profile, distinguish regions of the brain that are over-represented in the corresponding evolutionary timescale. We argue that the conclusions one can draw on evolution of twelve major brain regions from such a molecular level analysis supplements existing knowledge of mouse brain evolution and introduces new quantitative tools, especially for comparative studies, when AGEA-like data sets for other species become available. Using the functional role of the genes representational of a certain evolutionary timescale and brain region we compare and contrast, wherever possible, our observations with existing knowledge in evolutionary neuroanatomy.

q-bio.QM↗

arXiv2011

SLIQ: Simple Linear Inequalities for Efficient Contig Scaffolding

Scaffolding is an important subproblem in "de novo" genome assembly in which mate pair data are used to construct a linear sequence of contigs separated by gaps. Here we present SLIQ, a set of simple linear inequalities derived from the geometry of contigs on the line that can be used to predict the relative positions and orientations of contigs from individual mate pair reads and thus produce a contig digraph. The SLIQ inequalities can also filter out unreliable mate pairs and can be used as a preprocessing step for any scaffolding algorithm. We tested the SLIQ inequalities on five real data sets ranging in complexity from simple bacterial genomes to complex mammalian genomes and compared the results to the majority voting procedure used by many other scaffolding algorithms. SLIQ predicted the relative positions and orientations of the contigs with high accuracy in all cases and gave more accurate position predictions than majority voting for complex genomes, in particular the human genome. Finally, we present a simple scaffolding algorithm that produces linear scaffolds given a contig digraph. We show that our algorithm is very efficient compared to other scaffolding algorithms while maintaining high accuracy in predicting both contig positions and orientations for real data sets.

q-bio.GN↗

arXiv2011

Theoretical analysis of the role of chromatin interactions in long-range action of enhancers and insulators

Long-distance regulatory interactions between enhancers and their target genes are commonplace in higher eukaryotes. Interposed boundaries or insulators are able to block these long distance regulatory interactions. The mechanistic basis for insulator activity and how it relates to enhancer action-at-a-distance remains unclear. Here we explore the idea that topological loops could simultaneously account for regulatory interactions of distal enhancers and the insulating activity of boundary elements. We show that while loop formation is not in itself sufficient to explain action at a distance, incorporating transient non-specific and moderate attractive interactions between the chromatin fibers strongly enhances long-distance regulatory interactions and is sufficient to generate a euchromatin-like state. Under these same conditions, the subdivision of the loop into two topologically independent loops by insulators inhibits inter-domain interactions. The underlying cause of this effect is a suppression of crossings in the contact map at intermediate distances. Thus our model simultaneously accounts for regulatory interactions at a distance and the insulator activity of boundary elements. This unified model of the regulatory roles of chromatin loops makes several testable predictions that could be confronted with \emph{in vitro} experiments, as well as genomic chromatin conformation capture and fluorescent microscopic approaches.

q-bio.SC↗

arXiv2010

Statistical mechanics of transcription-factor binding site discovery using Hidden Markov Models

Hidden Markov Models (HMMs) are a commonly used tool for inference of transcription factor (TF) binding sites from DNA sequence data. We exploit the mathematical equivalence between HMMs for TF binding and the "inverse" statistical mechanics of hard rods in a one-dimensional disordered potential to investigate learning in HMMs. We derive analytic expressions for the Fisher information, a commonly employed measure of confidence in learned parameters, in the biologically relevant limit where the density of binding sites is low. We then use techniques from statistical mechanics to derive a scaling principle relating the specificity (binding energy) of a TF to the minimum amount of training data necessary to learn it.

cond-mat.stat-mech↗

arXiv2007

Shape, size and robustness: feasible regions in the parameter space of biochemical networks

The concept of robustness of regulatory networks has been closely related to the nature of the interactions among genes, and the capability of pattern maintenance or reproducibility. Defining this robustness property is a challenging task, but mathematical models have often associated it to the volume of the space of admissible parameters. Not only the volume of the space but also its topology and geometry contain information on essential aspects of the network, including feasible pathways, switching between two parallel pathways or distinct/disconnected active regions of parameters. A general method is presented here to characterize the space of admissible parameters, by writing it as a semi-algebraic set, and then theoretically analyzing its topology and geometry, as well as volume. This method provides a more objective and complete measure of the robustness of a developmental module. As an illustration, the segment polarity gene network is analyzed.

q-bio.MN↗

arXiv2007

Epigenetic Chromatin Silencing: Bistability and Front Propagation

The role of post-translational modification of histones in eukaryotic gene regulation is well recognized. Epigenetic silencing of genes via heritable chromatin modifications plays a major role in cell fate specification in higher organisms. We formulate a coarse-grained model of chromatin silencing in yeast and study the conditions under which the system becomes bistable, allowing for different epigenetic states. We also study the dynamics of the boundary between the two locally stable states of chromatin: silenced and unsilenced. The model could be of use in guiding the discussion on chromatin silencing in general. In the context of silencing in budding yeast, it helps us understand the phenotype of various mutants, some of which may be non-trivial to see without the help of a mathematical model. One such example is a mutation that reduces the rate of background acetylation of particular histone side-chains that competes with the deacetylation by Sir2p. The resulting negative feedback due to a Sir protein depletion effect gives rise to interesting counter-intuitive consequences. Our mathematical analysis brings forth the different dynamical behaviors possible within the same molecular model and guides the formulation of more refined hypotheses that could be addressed experimentally.

q-bio.MN↗