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Tushar Vaidya

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3 papers

2 author rows

AAAI Conference 2023 Conference Paper

Mean Estimation of Truncated Mixtures of Two Gaussians: A Gradient Based Approach

Sai Ganesh Nagarajan
Gerasimos Palaiopanos
Ioannis Panageas
Tushar Vaidya
Samson Yu

Even though data is abundant, it is often subjected to some form of censoring or truncation which inherently creates biases. Removing such biases and performing parameter estimation is a classical challenge in Statistics. In this paper, we focus on the problem of estimating the means of a mixture of two balanced d-dimensional Gaussians when the samples are prone to truncation. A recent theoretical study on the performance of the Expectation-Maximization (EM) algorithm for the aforementioned problem showed EM almost surely converges for d=1 and exhibits local convergence for d>1 to the true means. Nevertheless, the EM algorithm for the case of truncated mixture of two Gaussians is not easy to implement as it requires solving a set of nonlinear equations at every iteration which makes the algorithm impractical. In this work, we propose a gradient based variant of the EM algorithm that has global convergence guarantees when d=1 and local convergence for d>1 to the true means. Moreover, the update rule at every iteration is easy to compute which makes the proposed method practical. We also provide numerous experiments to obtain more insights into the effect of truncation on the convergence to the true parameters in high dimensions.

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ICRA Conference 2020 Conference Paper

Topological Mapping for Manhattan-like Repetitive Environments

Sai Shubodh Puligilla
Satyajit Tourani
Tushar Vaidya
Udit Singh Parihar
Ravi Kiran Sarvadevabhatla
K. Madhava Krishna

We showcase a topological mapping framework for a challenging indoor warehouse setting. At the most abstract level, the warehouse is represented as a Topological Graph where the nodes of the graph represent a particular warehouse topological construct (e. g. rackspace, corridor) and the edges denote the existence of a path between two neighbouring nodes or topologies. At the intermediate level, the map is represented as a Manhattan Graph where the nodes and edges are characterized by Manhattan properties and as a Pose Graph at the lower-most level of detail. The topological constructs are learned via a Deep Convolutional Network while the relational properties between topological instances are learnt via a Siamese-style Neural Network. In the paper, we show that maintaining abstractions such as Topological Graph and Manhattan Graph help in recovering an accurate Pose Graph starting from a highly erroneous and unoptimized Pose Graph. We show how this is achieved by embedding topological and Manhattan relations as well as Manhattan Graph aided loop closure relations as constraints in the backend Pose Graph optimization framework. The recovery of near ground-truth Pose Graph on real-world indoor warehouse scenes vindicate the efficacy of the proposed framework.

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AAMAS Conference 2018 Conference Paper

Learning Agents in Financial Markets: Consensus Dynamics on Volatility

Tushar Vaidya
Carlos Murguia
Georgios Piliouras

Black-Scholes (BS) is the standard mathematical model for European option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes, however, in practice it varies. How do traders come to learn these parameters? We introduce and analyze the convergence properties of natural models of learning agents, in which they update their beliefs about the true implied volatility based on the opinions of other traders.

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