Preference-based Pure Exploration

We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $\mathcal{C}$ and our the goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower bound on the sample complexity for identifying the most preferred policy with confidence level $1-\delta$. Our lower bound elicits the role played by the geometry of the preference cone and punctuates the difference in hardness compared to existing best-arm identification variants of the problem. We further explicate this geometry when rewards follow Gaussian distributions. We then provide a convex relaxation of the lower bound. and leverage it to design Preference-based Track and Stop (PreTS) algorithm that identifies the most preferred policy. Finally, we show that sample complexity of PreTS is asymptotically tight by deriving a new concentration inequality for vector-valued rewards.

Differentially Private High Dimensional Bandits

We consider a high-dimensional stochastic contextual linear bandit problem when the parameter vector is $s_{0}$-sparse and the decision maker is subject to privacy constraints under both central and local models of differential privacy. We present PrivateLASSO, a differentially private LASSO bandit algorithm. PrivateLASSO is based on two sub-routines: (i) a sparse hard-thresholding-based privacy mechanism and (ii) an episodic thresholding rule for identifying the support of the parameter $\theta$. We prove minimax private lower bounds and establish privacy and utility guarantees for PrivateLASSO for the central model under standard assumptions.

An Efficient Deep Convolutional Neural Network Model For Yoga Pose Recognition Using Single Images

Pose recognition deals with designing algorithms to locate human body joints in a 2D/3D space and run inference on the estimated joint locations for predicting the poses. Yoga poses consist of some very complex postures. It imposes various challenges on the computer vision algorithms like occlusion, inter-class similarity, intra-class variability, viewpoint complexity, etc. This paper presents YPose, an efficient deep convolutional neural network (CNN) model to recognize yoga asanas from RGB images. The proposed model consists of four steps as follows: (a) first, the region of interest (ROI) is segmented using segmentation based approaches to extract the ROI from the original images; (b) second, these refined images are passed to a CNN architecture based on the backbone of EfficientNets for feature extraction; (c) third, dense refinement blocks, adapted from the architecture of densely connected networks are added to learn more diversified features; and (d) fourth, global average pooling and fully connected layers are applied for the classification of the multi-level hierarchy of the yoga poses. The proposed model has been tested on the Yoga-82 dataset. It is a publicly available benchmark dataset for yoga pose recognition. Experimental results show that the proposed model achieves the state-of-the-art on this dataset. The proposed model obtained an accuracy of 93.28%, which is an improvement over the earlier state-of-the-art (79.35%) with a margin of approximately 13.9%. The code will be made publicly available.

Non-Stationary Streaming PCA

We consider the problem of streaming principal component analysis (PCA) when the observations are noisy and generated in a non-stationary environment. Given $T$, $p$-dimensional noisy observations sampled from a non-stationary variant of the spiked covariance model, our goal is to construct the best linear $k$-dimensional subspace of the terminal observations. We study the effect of non-stationarity by establishing a lower bound on the number of samples and the corresponding recovery error obtained by any algorithm. We establish the convergence behaviour of the noisy power method using a novel proof technique which maybe of independent interest. We conclude that the recovery guarantee of the noisy power method matches the fundamental limit, thereby generalizing existing results on streaming PCA to a non-stationary setting.