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Jun 1

Fixed-Budget Differentially Private Best Arm Identification

We study best arm identification (BAI) in linear bandits in the fixed-budget regime under differential privacy constraints, when the arm rewards are supported on the unit interval. Given a finite budget T and a privacy parameter varepsilon>0, the goal is to minimise the error probability in finding the arm with the largest mean after T sampling rounds, subject to the constraint that the policy of the decision maker satisfies a certain {\em varepsilon-differential privacy} (varepsilon-DP) constraint. We construct a policy satisfying the varepsilon-DP constraint (called {\sc DP-BAI}) by proposing the principle of {\em maximum absolute determinants}, and derive an upper bound on its error probability. Furthermore, we derive a minimax lower bound on the error probability, and demonstrate that the lower and the upper bounds decay exponentially in T, with exponents in the two bounds matching order-wise in (a) the sub-optimality gaps of the arms, (b) varepsilon, and (c) the problem complexity that is expressible as the sum of two terms, one characterising the complexity of standard fixed-budget BAI (without privacy constraints), and the other accounting for the varepsilon-DP constraint. Additionally, we present some auxiliary results that contribute to the derivation of the lower bound on the error probability. These results, we posit, may be of independent interest and could prove instrumental in proving lower bounds on error probabilities in several other bandit problems. Whereas prior works provide results for BAI in the fixed-budget regime without privacy constraints or in the fixed-confidence regime with privacy constraints, our work fills the gap in the literature by providing the results for BAI in the fixed-budget regime under the varepsilon-DP constraint.

  • 4 authors
·
Jan 17, 2024

Hamba: Single-view 3D Hand Reconstruction with Graph-guided Bi-Scanning Mamba

3D Hand reconstruction from a single RGB image is challenging due to the articulated motion, self-occlusion, and interaction with objects. Existing SOTA methods employ attention-based transformers to learn the 3D hand pose and shape, yet they do not fully achieve robust and accurate performance, primarily due to inefficiently modeling spatial relations between joints. To address this problem, we propose a novel graph-guided Mamba framework, named Hamba, which bridges graph learning and state space modeling. Our core idea is to reformulate Mamba's scanning into graph-guided bidirectional scanning for 3D reconstruction using a few effective tokens. This enables us to efficiently learn the spatial relationships between joints for improving reconstruction performance. Specifically, we design a Graph-guided State Space (GSS) block that learns the graph-structured relations and spatial sequences of joints and uses 88.5% fewer tokens than attention-based methods. Additionally, we integrate the state space features and the global features using a fusion module. By utilizing the GSS block and the fusion module, Hamba effectively leverages the graph-guided state space features and jointly considers global and local features to improve performance. Experiments on several benchmarks and in-the-wild tests demonstrate that Hamba significantly outperforms existing SOTAs, achieving the PA-MPVPE of 5.3mm and F@15mm of 0.992 on FreiHAND. At the time of this paper's acceptance, Hamba holds the top position, Rank 1 in two Competition Leaderboards on 3D hand reconstruction. Project Website: https://humansensinglab.github.io/Hamba/

A Neural Anthropometer Learning from Body Dimensions Computed on Human 3D Meshes

Human shape estimation has become increasingly important both theoretically and practically, for instance, in 3D mesh estimation, distance garment production and computational forensics, to mention just a few examples. As a further specialization, Human Body Dimensions Estimation (HBDE) focuses on estimating human body measurements like shoulder width or chest circumference from images or 3D meshes usually using supervised learning approaches. The main obstacle in this context is the data scarcity problem, as collecting this ground truth requires expensive and difficult procedures. This obstacle can be overcome by obtaining realistic human measurements from 3D human meshes. However, a) there are no well established methods to calculate HBDs from 3D meshes and b) there are no benchmarks to fairly compare results on the HBDE task. Our contribution is twofold. On the one hand, we present a method to calculate right and left arm length, shoulder width, and inseam (crotch height) from 3D meshes with focus on potential medical, virtual try-on and distance tailoring applications. On the other hand, we use four additional body dimensions calculated using recently published methods to assemble a set of eight body dimensions which we use as a supervision signal to our Neural Anthropometer: a convolutional neural network capable of estimating these dimensions. To assess the estimation, we train the Neural Anthropometer with synthetic images of 3D meshes, from which we calculated the HBDs and observed that the network's overall mean estimate error is 20.89 mm (relative error of 2.84\%). The results we present are fully reproducible and establish a fair baseline for research on the task of HBDE, therefore enabling the community with a valuable method.

  • 2 authors
·
Oct 6, 2021