我们严格地证明，如果目标函数具有组成结构，那么深层的过程先验可以超越高斯工艺先验。为此，我们研究了连续回归模型中高斯过程回归后收缩率的信息理论下限。我们表明，如果真实函数是广义的加性函数，那么基于任何平均零高斯过程的后验只能以严格慢的速率恢复真相，而该速率比最小值速率慢了，该因子在样品中多项式次优的因素。尺寸$ n $。

我们提出了一种变分贝叶斯比例危险模型，用于预测和可变选择的关于高维存活数据。我们的方法基于平均场变分近似，克服了MCMC的高计算成本，而保留有用的特征，提供优异的点估计，并通过后夹层概念提供可变选择的自然机制。我们提出的方法的性能通过广泛的仿真进行评估，并与其他最先进的贝叶斯变量选择方法进行比较，展示了可比或更好的性能。最后，我们展示了如何在两个转录组数据集上使用所提出的方法进行审查的生存结果，其中我们识别具有预先存在的生物解释的基因。

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.

Modelling and forecasting real-life human behaviour using online social media is an active endeavour of interest in politics, government, academia, and industry. Since its creation in 2006, Twitter has been proposed as a potential laboratory that could be used to gauge and predict social behaviour. During the last decade, the user base of Twitter has been growing and becoming more representative of the general population. Here we analyse this user base in the context of the 2021 Mexican Legislative Election. To do so, we use a dataset of 15 million election-related tweets in the six months preceding election day. We explore different election models that assign political preference to either the ruling parties or the opposition. We find that models using data with geographical attributes determine the results of the election with better precision and accuracy than conventional polling methods. These results demonstrate that analysis of public online data can outperform conventional polling methods, and that political analysis and general forecasting would likely benefit from incorporating such data in the immediate future. Moreover, the same Twitter dataset with geographical attributes is positively correlated with results from official census data on population and internet usage in Mexico. These findings suggest that we have reached a period in time when online activity, appropriately curated, can provide an accurate representation of offline behaviour.

Representing and synthesizing novel views in real-world dynamic scenes from casual monocular videos is a long-standing problem. Existing solutions typically approach dynamic scenes by applying geometry techniques or utilizing temporal information between several adjacent frames without considering the underlying background distribution in the entire scene or the transmittance over the ray dimension, limiting their performance on static and occlusion areas. Our approach $\textbf{D}$istribution-$\textbf{D}$riven neural radiance fields offers high-quality view synthesis and a 3D solution to $\textbf{D}$etach the background from the entire $\textbf{D}$ynamic scene, which is called $\text{D}^4$NeRF. Specifically, it employs a neural representation to capture the scene distribution in the static background and a 6D-input NeRF to represent dynamic objects, respectively. Each ray sample is given an additional occlusion weight to indicate the transmittance lying in the static and dynamic components. We evaluate $\text{D}^4$NeRF on public dynamic scenes and our urban driving scenes acquired from an autonomous-driving dataset. Extensive experiments demonstrate that our approach outperforms previous methods in rendering texture details and motion areas while also producing a clean static background. Our code will be released at https://github.com/Luciferbobo/D4NeRF.

Code generation models have achieved impressive performance. However, they tend to be brittle as slight edits to a prompt could lead to very different generations; these robustness properties, critical for user experience when deployed in real-life applications, are not well understood. Most existing works on robustness in text or code tasks have focused on classification, while robustness in generation tasks is an uncharted area and to date there is no comprehensive benchmark for robustness in code generation. In this paper, we propose ReCode, a comprehensive robustness evaluation benchmark for code generation models. We customize over 30 transformations specifically for code on docstrings, function and variable names, code syntax, and code format. They are carefully designed to be natural in real-life coding practice, preserve the original semantic meaning, and thus provide multifaceted assessments of a model's robustness performance. With human annotators, we verified that over 90% of the perturbed prompts do not alter the semantic meaning of the original prompt. In addition, we define robustness metrics for code generation models considering the worst-case behavior under each type of perturbation, taking advantage of the fact that executing the generated code can serve as objective evaluation. We demonstrate ReCode on SOTA models using HumanEval, MBPP, as well as function completion tasks derived from them. Interesting observations include: better robustness for CodeGen over InCoder and GPT-J; models are most sensitive to syntax perturbations; more challenging robustness evaluation on MBPP over HumanEval.

Modeling perception sensors is key for simulation based testing of automated driving functions. Beyond weather conditions themselves, sensors are also subjected to object dependent environmental influences like tire spray caused by vehicles moving on wet pavement. In this work, a novel modeling approach for spray in lidar data is introduced. The model conforms to the Open Simulation Interface (OSI) standard and is based on the formation of detection clusters within a spray plume. The detections are rendered with a simple custom ray casting algorithm without the need of a fluid dynamics simulation or physics engine. The model is subsequently used to generate training data for object detection algorithms. It is shown that the model helps to improve detection in real-world spray scenarios significantly. Furthermore, a systematic real-world data set is recorded and published for analysis, model calibration and validation of spray effects in active perception sensors. Experiments are conducted on a test track by driving over artificially watered pavement with varying vehicle speeds, vehicle types and levels of pavement wetness. All models and data of this work are available open source.

With the success of neural volume rendering in novel view synthesis, neural implicit reconstruction with volume rendering has become popular. However, most methods optimize per-scene functions and are unable to generalize to novel scenes. We introduce VolRecon, a generalizable implicit reconstruction method with Signed Ray Distance Function (SRDF). To reconstruct with fine details and little noise, we combine projection features, aggregated from multi-view features with a view transformer, and volume features interpolated from a coarse global feature volume. A ray transformer computes SRDF values of all the samples along a ray to estimate the surface location, which are used for volume rendering of color and depth. Extensive experiments on DTU and ETH3D demonstrate the effectiveness and generalization ability of our method. On DTU, our method outperforms SparseNeuS by about 30% in sparse view reconstruction and achieves comparable quality as MVSNet in full view reconstruction. Besides, our method shows good generalization ability on the large-scale ETH3D benchmark. Project page: https://fangjinhuawang.github.io/VolRecon.

Recent efforts in Neural Rendering Fields (NeRF) have shown impressive results on novel view synthesis by utilizing implicit neural representation to represent 3D scenes. Due to the process of volumetric rendering, the inference speed for NeRF is extremely slow, limiting the application scenarios of utilizing NeRF on resource-constrained hardware, such as mobile devices. Many works have been conducted to reduce the latency of running NeRF models. However, most of them still require high-end GPU for acceleration or extra storage memory, which is all unavailable on mobile devices. Another emerging direction utilizes the neural light field (NeLF) for speedup, as only one forward pass is performed on a ray to predict the pixel color. Nevertheless, to reach a similar rendering quality as NeRF, the network in NeLF is designed with intensive computation, which is not mobile-friendly. In this work, we propose an efficient network that runs in real-time on mobile devices for neural rendering. We follow the setting of NeLF to train our network. Unlike existing works, we introduce a novel network architecture that runs efficiently on mobile devices with low latency and small size, i.e., saving $15\times \sim 24\times$ storage compared with MobileNeRF. Our model achieves high-resolution generation while maintaining real-time inference for both synthetic and real-world scenes on mobile devices, e.g., $18.04$ms (iPhone 13) for rendering one $1008\times756$ image of real 3D scenes. Additionally, we achieve similar image quality as NeRF and better quality than MobileNeRF (PSNR $26.15$ vs. $25.91$ on the real-world forward-facing dataset).

Neural Radiance Fields (NeRF) have demonstrated superior novel view synthesis performance but are slow at rendering. To speed up the volume rendering process, many acceleration methods have been proposed at the cost of large memory consumption. To push the frontier of the efficiency-memory trade-off, we explore a new perspective to accelerate NeRF rendering, leveraging a key fact that the viewpoint change is usually smooth and continuous in interactive viewpoint control. This allows us to leverage the information of preceding viewpoints to reduce the number of rendered pixels as well as the number of sampled points along the ray of the remaining pixels. In our pipeline, a low-resolution feature map is rendered first by volume rendering, then a lightweight 2D neural renderer is applied to generate the output image at target resolution leveraging the features of preceding and current frames. We show that the proposed method can achieve competitive rendering quality while reducing the rendering time with little memory overhead, enabling 30FPS at 1080P image resolution with a low memory footprint.