Capturing multimodal natures is essential for stochastic pedestrian
trajectory prediction, to infer a finite set of future trajectories. The
inferred trajectories are based on observation paths and the latent vectors of
potential decisions of pedestrians in the inference step. However, stochastic
approaches provide varying results for the same data and parameter settings,
due to the random sampling of the latent vector. In this paper, we analyze the
problem by reconstructing and comparing probabilistic distributions from
prediction samples and socially-acceptable paths, respectively. Through this
analysis, we observe that the inferences of all stochastic models are biased
toward the random sampling, and fail to generate a set of realistic paths from
finite samples. The problem cannot be resolved unless an infinite number of
samples is available, which is infeasible in practice. We introduce that the
Quasi-Monte Carlo (QMC) method, ensuring uniform coverage on the sampling
space, as an alternative to the conventional random sampling. With the same
finite number of samples, the QMC improves all the multimodal prediction
results. We take an additional step ahead by incorporating a learnable sampling
network into the existing networks for trajectory prediction. For this purpose,
we propose the Non-Probability Sampling Network (NPSN), a very small network
(~5K parameters) that generates purposive sample sequences using the past paths
of pedestrians and their social interactions. Extensive experiments confirm
that NPSN can significantly improve both the prediction accuracy (up to 60%)
and reliability of the public pedestrian trajectory prediction benchmark. Code
is publicly available at this https URL .

研究了随机方法在预测行人轨迹中存在的偏差问题，并提出了 Quasi-Monte Carlo 方法以及 Non-Probability Sampling Network 作为改进方案，通过实验验证了该方案可以显著提高行人轨迹预测的准确性和可靠性。

基于非概率抽样网络的随机人体轨迹预测

Non-Probability Sampling Network for Stochastic Human Trajectory  Prediction

Deterministic approaches using iterative optimisation have been historically
successful in diffeomorphic image registration (DiffIR). Although these
approaches are highly accurate, they typically carry a significant
computational burden. Recent developments in stochastic approaches based on
deep learning have achieved sub-second runtimes for DiffIR with competitive
registration accuracy, offering a fast alternative to conventional iterative
methods. In this paper, we attempt to reduce this difference in speed whilst
retaining the performance advantage of iterative approaches in DiffIR. We first
propose a simple iterative scheme that functionally composes intermediate
non-stationary velocity fields to handle large deformations in images whilst
guaranteeing diffeomorphisms in the resultant deformation. We then propose a
convex optimisation model that uses a regularisation term of arbitrary order to
impose smoothness on these velocity fields and solve this model with a fast
algorithm that combines Nesterov gradient descent and the alternating direction
method of multipliers (ADMM). Finally, we leverage the computational power of
GPU to implement this accelerated ADMM solver on a 3D cardiac MRI dataset,
further reducing runtime to less than 2 seconds. In addition to producing
strictly diffeomorphic deformations, our methods outperform both
state-of-the-art deep learning-based and iterative DiffIR approaches in terms
of dice and Hausdorff scores, with speed approaching the inference time of deep
learning-based methods.

本文提出了一种使用简单的迭代方案和基于 Nesterov 梯度下降和多重乘法交替方向法的快速算法解决难以处理的大形变的非静止速度场，同时利用 GPU 加速实现加速 ADMM 求解器，优于基于深度学习的和迭代 DiffIR 方法，并在精度方面取得了更好的表现。

用于快速同胚图像配准的 Nesterov 加速 ADMM

Nesterov Accelerated ADMM for Fast Diffeomorphic Image Registration

Variational inference has experienced a recent surge in popularity owing to
stochastic approaches, which have yielded practical tools for a wide range of
model classes. A key benefit is that stochastic variational inference obviates
the tedious process of deriving analytical expressions for closed-form variable
updates. Instead, one simply needs to derive the gradient of the log-posterior,
which is often much easier. Yet for certain model classes, the log-posterior
itself is difficult to optimize using standard gradient techniques. One such
example are random field models, where optimization based on gradient
linearization has proven popular, since it speeds up convergence significantly
and can avoid poor local optima. In this paper we propose stochastic
variational inference with gradient linearization (SVIGL). It is similarly
convenient as standard stochastic variational inference - all that is required
is a local linearization of the energy gradient. Its benefit over stochastic
variational inference with conventional gradient methods is a clear improvement
in convergence speed, while yielding comparable or even better variational
approximations in terms of KL divergence. We demonstrate the benefits of SVIGL
in three applications: Optical flow estimation, Poisson-Gaussian denoising, and
3D surface reconstruction.

本文提出了随机梯度线性化变分推断，并通过三个应用案例展示了在收敛速度和 KL 散度方面相对于传统梯度方法的明显优势。