I am currently a 4th year PhD student, at Applied Maths department at Brown University. My research interests are data analysis, machine learning and their applications in neuroscience.
I work with Professor Matthew Harrison.
We develop statistical software for neuroscientists to use for large amounts of data they have recorded in order to check their scientific hypothesis.
Neuronal firing rate can transmit a high level of neural information. Therefore finding a good solution to estimate it from spike trains is a very important problem. But this problem is also very complex because of the high variability of neural response and because spike data gives only a sparse observation of the underlying firing rate. All current techniques that tackle this problem have drawbacks.
Specifically we are working on:
-Mathematically modeling neuronal firing rate- this is a nonparametric regression problem and a problem of constructing simultaneous confidence bands.
-Quantifying the change in neural firing rate in various conditions in hippocampal place cells, major problem being the change of covariates (i.e. rat’s positions) between conditions.
Key tools that we use include kernel density estimation, parametric and nonparametric regression, confidence bands, Bonferonni correction, multiple hypothesis testing, wavelets, Gaussian Processes…
The data we work on are spike train recordings from a number of neurons in the hippocampus of a rat exploring a two-dimensional maze.
This is a part of the Buzaki's lab research on hippocampal place cells in rats. This lab is doing a cutting-edge research on hippocampus. Place cells are neurons within hippocampus that fire only when the rat is at certain locations in the environment. Hippocampus is associated with spatial navigation and memory.
-Data: Local field potentials and spike trains simultaneously recorded in a number of neurons in both PFC and Caudate Nucleus (two regions in the brain), in two monkeys, during a trial-and-error learning task. Data was collected every day over a period of about two months and is provided to us by Wael Asaad.
-Context: We are interested in the relationship between the two regions- PFC and Caudate. The motivation for this is the assumption that PFC-Caudate conveys the information necessary for a monkey to solve a temporal credit assignment problem. Indeed, it is believed that PFC-Caudate interaction changes over the course of a learning trial, especially with regard to what happens at the time of feedback.
-Goal: Our goal is two-fold. First, find a good way to represent the communication between the two regions. One of the possibilities would be coherence measure between spikes in PFC and local field potentials in Caudate. Second, we would like to mathematically rigorously, quantify how is this relationship being changed at different stages of learning.
-Key tools: Kernel Density Estimation, Confidence Intervals, Spectral Analysis, Fourier Transform, Wavelets.
Fluorescent calcium imaging is a state of the art tool for simultaneously monitoring activity of thousands of neurons. Using calcium fluorescence to study neural dynamic is becoming increasingly popular. One of the central problem is deducing a neural network connectivity. However, inferring signals of interest, i.e. spike trains and/or intracellular calcium concentrations, from the fluorescent calcium imaging is problematic because of the noise, nonlinearities and slow imaging rate.
We tackled this problem of network inference. Data we worked on were simultaneous recordings of the fluorescence levels for a network of 100 neurons, collected over a period of time lasting one hour. Based on this data, our goal was to infer directed connections between neurons in the network.
We formulated a nonlinear state-space model to describe the system- spike trains and intracellular calcium concentrations being the hidden variable and fluorescence measurements being the observed states- as well as the equations that govern it. Elements of the connectivity matrix ( matrix of synaptic weights between neurons, size 100 by 100), were part of the set of parameters of the model. Therefore, we had a parameter estimation problem, with incomplete observation. To solve it, we implemented expectation-maximization algorithm. In the E-step we implemented a particle filter and in the M-step we solved optimization problems using a optimization package that solves L1-regularization problems.
Key tools: Probabilistic Graphical Models, Sequential Monte Carlo methods, L1-regularization.
Current object recognition models face a tradeoff between selectivity with respect to objects and invariance with respect to pose parameters. The object recognition model we work with is HMAX, a hierarchical model of layers of simple and complex cells, developed by Poggio Lab to recognize visual objects and scenes.
Our goal was to achieve a better invariance/selectivity compromise of the HMAX by implementing ideas inspired by biology of the visual cortex. We proposed to include in the input to a given layer of HMAX some information about the state of the network beyond the layer(s) immediately adjacent to the layer under consideration. Specifically, we proposed to use a mechanism based on a suitable non-linear function of the network activity along multiple diverging-converging paths spanning several layers. In graph-theoretical terms, this mechanism is, roughly, equivalent to the computation of the level of activation of a specific type of network motifs, referred to, e.g. in systems biology (computational genomics), as multi-parallel or diamond-shaped. This mechanism enables the model to implement context-dependent calculations consistent with simple Gestalt laws. We argued that such motif-based computation may be made available to cortical dynamics by the high sensitivity of cortical cells to near-sychronous input and by the abundance of converging-diverging cortical synaptic pathways giving rise to such synchronous input. Our proposal was illustrated by numerical experiments with the HMAX model and supplemented with motif-based calculation. We showed that the inclusion of a suitable motif term in the HMAX model allows for better performance, in particular on cluttered scenes.
-Use of data-mining tools to search for patterns in the grades and make prediction on the performance of students.
-Development of a software in Matlab/R implementing the above.
-Key tools: Regression, SVM, decision trees, PCA, clustering.