Search

Bayesian inference is conceptually elegant, but calculating posterior expectations can entail a heavy computational cost. Monte Carlo methods are reliable and supported by strong asymptotic guarantees, but do not leverage smoothness of the integrand. Solving Stein equations has emerged as a possible alternative, providing a framework for numerical approximation of posterior expectations in which smoothness can be exploited. However, existing numerical methods for Stein equations are associated with high computational cost due to the need to solve large linear systems. This paper considers the combination of iterative linear solvers and preconditioning strategies to obtain fast approximate solutions of Stein equations. Our main finding is that these methods can be effective, but that the performance of different preconditioning strategies is context-dependent, so that no single strategy can be universally preferred.

The Sequential Recommendation modeling paradigm is shifting from Transformer to Mamba architecture, which comprises two generations: Mamba1, based on the State Space Model (SSM), and Mamba2, based on State Space Duality (SSD). Although SSD offers superior computational efficiency compared to SSM, it suffers performance degradation in sequential recommendation tasks, especially in low-dimensional scenarios that are critical for these tasks. Considering that time-aware enhancement methods are commonly employed to mitigate performance loss, our analysis reveals that the performance decline of SSD can similarly be fundamentally compensated by leveraging mechanisms in time-aware methods. Thus, we propose integrating time-awareness into the SSD framework to address these performance issues. However, integrating current time-aware methods, modeled after TiSASRec, into SSD faces the following challenges: 1) the complexity of integrating these transformer-based mechanisms with the SSD architecture, and 2) the computational inefficiency caused by the need for dimensionality expansion of time-difference modeling. To overcome these challenges, we introduce a novel Time-aware Structured Masked Matrix that efficiently incorporates time-aware capabilities into SSD. Building on this, we propose Time-Aware Mamba for Recommendation (TiM4Rec), which mitigates performance degradation in low-dimensional SSD contexts while preserving computational efficiency. This marks the inaugural application of a time-aware enhancement method specifically tailored for the Mamba architecture within the domain of sequential recommendation. Extensive experiments conducted on three real-world datasets demonstrate the superiority of our approach. The code for our model is accessible at https://github.com/AlwaysFHao/TiM4Rec.

In the realm of image composition, generating realistic shadow for the inserted foreground remains a formidable challenge. Previous works have developed image-to-image translation models which are trained on paired training data. However, they are struggling to generate shadows with accurate shapes and intensities, hindered by data scarcity and inherent task complexity. In this paper, we resort to foundation model with rich prior knowledge of natural shadow images. Specifically, we first adapt ControlNet to our task and then propose intensity modulation modules to improve the shadow intensity. Moreover, we extend the small-scale DESOBA dataset to DESOBAv2 using a novel data acquisition pipeline. Experimental results on both DESOBA and DESOBAv2 datasets as well as real composite images demonstrate the superior capability of our model for shadow generation task. The dataset, code, and model are released at https://github.com/bcmi/Object-Shadow-Generation-Dataset-DESOBAv2., Comment: accepted by CVPR2024

Traditional dose selection for oncology registration trials typically employs a one- or two-step single maximum tolerated dose (MTD) approach. However, this approach may not be appropriate for molecularly targeted therapy that tends to have toxicity profiles that are markedly different to cytotoxic agents. The US Food and Drug Administration launched Project Optimus to reform dose optimization in oncology drug development and has recently released a related Guidance for Industry. In response to these initiatives, we propose a "three steps towards dose optimization" procedure and discuss the details in dose optimization designs and analyses in this manuscript. The first step is dose-escalation to identify the MTD or maximum administered dose with an efficient hybrid design, which can offer good overdose control and increases the likelihood of the recommended MTD being close to the true MTD. The second step is the selection of appropriate recommended doses for expansion (RDEs), based on all available data including emerging safety, pharmacokinetics, pharmacodynamics, and other biomarker information. The third step is dose optimization, which uses data from a randomized fractional factorial design with multiple RDEs explored in multiple tumor cohorts during the expansion phase to ensure a feasible dose is selected for registration trials, and that the tumor type most sensitive to the investigative treatment is identified. We believe using this three-step approach can increase the likelihood of selecting the optimal dose for registration trial, one that demonstrates a balanced safety profile while retaining much of the efficacy observed at the MTD., Comment: 22 pages, 7 figures and 2 tables

Image composition refers to inserting a foreground object into a background image to obtain a composite image. In this work, we focus on generating plausible shadow for the inserted foreground object to make the composite image more realistic. To supplement the existing small-scale dataset DESOBA, we create a large-scale dataset called DESOBAv2 by using object-shadow detection and inpainting techniques. Specifically, we collect a large number of outdoor scene images with object-shadow pairs. Then, we use pretrained inpainting model to inpaint the shadow region, resulting in the deshadowed images. Based on real images and deshadowed images, we can construct pairs of synthetic composite images and ground-truth target images. Dataset is available at https://github.com/bcmi/Object-Shadow-Generation-Dataset-DESOBAv2., Comment: arXiv admin note: text overlap with arXiv:2306.17358

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are explored, including model identifiability and flexibility in capturing heavy-tailed data that exhibit different directions of skewness over a wide range. Both frequentist and Bayesian methods are developed to infer parameters in the new distribution. Simulation studies are conducted to demonstrate satisfactory performance of both methods. By fitting the proposed model to simulated data and data from an application in hydrology, it is shown that the proposed flexible distribution is especially suitable for data containing extreme values in either direction, with the mode being a location parameter of interest. Using the proposed unimodal distribution, one can easily formulate a regression model concerning the mode of a response given covariates. We apply this model to data from an application in criminology to reveal interesting data features that are obscured by outliers. Computer programs for implementing all considered inference methods in the study are available at https://github.com/rh8liuqy/flexible_Gumbel., Comment: 15 pages, 3 figures

An inference procedure is proposed to provide consistent estimators of parameters in a modal regression model with a covariate prone to measurement error. A score-based diagnostic tool exploiting parametric bootstrap is developed to assess adequacy of parametric assumptions imposed on the regression model. The proposed estimation method and diagnostic tool are applied to synthetic data generated from simulation experiments and data from real-world applications to demonstrate their implementation and performance. These empirical examples illustrate the importance of adequately accounting for measurement error in the error-prone covariate when inferring the association between a response and covariates based on a modal regression model that is especially suitable for skewed and heavy-tailed response data., Comment: 17 pages, 3 figures

Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along with other parameters that allow for flexible shapes and tail behaviors. Sufficient conditions for posterior propriety under an improper prior on the mode parameter are derived. Following prior elicitation, regression analysis of simulated data and datasets from several real-life applications are conducted. Besides drawing inference for covariate effects that are easy to interpret, prediction and model selection under the proposed Bayesian modal regression framework are also considered. Evidence from these analyses suggest that the proposed inference procedures are very robust to outliers, enabling one to discover interesting covariate effects missed by mean or median regression, and to construct much tighter prediction intervals than those from mean or median regression. Computer programs for implementing the proposed Bayesian modal regression are available at https://github.com/rh8liuqy/Bayesian_modal_regression., Comment: 44 pages, 16 figures

Object placement assessment (OPA) aims to predict the rationality score of a composite image in terms of the placement (e.g., scale, location) of inserted foreground object. However, given a pair of scaled foreground and background, to enumerate all the reasonable locations, existing OPA model needs to place the foreground at each location on the background and pass the obtained composite image through the model one at a time, which is very time-consuming. In this work, we investigate a new task named as fast OPA. Specifically, provided with a scaled foreground and a background, we only pass them through the model once and predict the rationality scores for all locations. To accomplish this task, we propose a pioneering fast OPA model with several innovations (i.e., foreground dynamic filter, background prior transfer, and composite feature mimicking) to bridge the performance gap between slow OPA model and fast OPA model. Extensive experiments on OPA dataset show that our proposed fast OPA model performs on par with slow OPA model but runs significantly faster.

A multiplicative function $f$ is said to be resembling the M\"{o}bius function if $f$ is supported on the square-free integers, and $f(p)=\pm 1$ for each prime $p$. We prove $O$- and $\Omega$-results for the summatory function $\sum_{n\leq x} f(n)$ for a class of these $f$ studied by Aymone, and the point is that these $O$-results demonstrate cancellations better than the square-root saving. It is proved in particular that the summatory function is $O(x^{1/3+\varepsilon})$ under the Riemann Hypothesis. On the other hand it is proved to be $\Omega(x^{1/4})$ unconditionally. It is interesting to compare these with the corresponding results for the M\"{o}bius function., Comment: 16 pages