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We study the use of a deep Gaussian process (DGP) prior in a general nonlinear inverse problem satisfying certain regularity conditions. We prove that when the data arises from a true parameter $\theta^*$ with a compositional structure, the posterior induced by the DGP prior concentrates around $\theta^*$ as the number of observations increases. The DGP prior accounts for the unknown compositional structure through the use of a hierarchical structure prior. As examples, we show that our results apply to Darcy's problem of recovering the scalar diffusivity from a steady-state heat equation and the problem of determining the attenuation potential in a steady-state Schr\"{o}dinger equation. We further provide a lower bound, proving in Darcy's problem that typical Gaussian priors based on Whittle-Mat\'{e}rn processes (which ignore compositional structure) contract at a polynomially slower rate than the DGP prior for certain diffusivities arising from a generalised additive model.

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 Processing 是一門開源編程語言和與之配套的集成開發環境(IDE)的名稱。Processing 在電子藝術和視覺設計社區被用來教授編程基礎,并運用于大量的新媒體和互動藝術作品中。

Introduction This study explores the use of the latest You Only Look Once (YOLO V7) object detection method to enhance kidney detection in medical imaging by training and testing a modified YOLO V7 on medical image formats. Methods Study includes 878 patients with various subtypes of renal cell carcinoma (RCC) and 206 patients with normal kidneys. A total of 5657 MRI scans for 1084 patients were retrieved. 326 patients with 1034 tumors recruited from a retrospective maintained database, and bounding boxes were drawn around their tumors. A primary model was trained on 80% of annotated cases, with 20% saved for testing (primary test set). The best primary model was then used to identify tumors in the remaining 861 patients and bounding box coordinates were generated on their scans using the model. Ten benchmark training sets were created with generated coordinates on not-segmented patients. The final model used to predict the kidney in the primary test set. We reported the positive predictive value (PPV), sensitivity, and mean average precision (mAP). Results The primary training set showed an average PPV of 0.94 +/- 0.01, sensitivity of 0.87 +/- 0.04, and mAP of 0.91 +/- 0.02. The best primary model yielded a PPV of 0.97, sensitivity of 0.92, and mAP of 0.95. The final model demonstrated an average PPV of 0.95 +/- 0.03, sensitivity of 0.98 +/- 0.004, and mAP of 0.95 +/- 0.01. Conclusion Using a semi-supervised approach with a medical image library, we developed a high-performing model for kidney detection. Further external validation is required to assess the model's generalizability.

This study evaluates the ability of Large Language Model (LLM)-based Subpopulation Representative Models (SRMs) to generalize from empirical data, utilizing in-context learning with data from the 2016 and 2020 American National Election Studies. We explore generalization across response variables and demographic subgroups. While conditioning with empirical data improves performance on the whole, the benefit of in-context learning varies considerably across demographics, sometimes hurting performance for one demographic while helping performance for others. The inequitable benefits of in-context learning for SRM present a challenge for practitioners implementing SRMs, and for decision-makers who might come to rely on them. Our work highlights a need for fine-grained benchmarks captured from diverse subpopulations that test not only fidelity but generalization.

Computer vision models have been known to encode harmful biases, leading to the potentially unfair treatment of historically marginalized groups, such as people of color. However, there remains a lack of datasets balanced along demographic traits that can be used to evaluate the downstream fairness of these models. In this work, we demonstrate that diffusion models can be leveraged to create such a dataset. We first use a diffusion model to generate a large set of images depicting various occupations. Subsequently, each image is edited using inpainting to generate multiple variants, where each variant refers to a different perceived race. Using this dataset, we benchmark several vision-language models on a multi-class occupation classification task. We find that images generated with non-Caucasian labels have a significantly higher occupation misclassification rate than images generated with Caucasian labels, and that several misclassifications are suggestive of racial biases. We measure a model's downstream fairness by computing the standard deviation in the probability of predicting the true occupation label across the different perceived identity groups. Using this fairness metric, we find significant disparities between the evaluated vision-and-language models. We hope that our work demonstrates the potential value of diffusion methods for fairness evaluations.

While the inverse probability of treatment weighting (IPTW) is a commonly used approach for treatment comparisons in observational data, the resulting estimates may be subject to bias and excessively large variance when there is lack of overlap in the propensity score distributions. By smoothly down-weighting the units with extreme propensity scores, overlap weighting (OW) can help mitigate the bias and variance issues associated with IPTW. Although theoretical and simulation results have supported the use of OW with continuous and binary outcomes, its performance with right-censored survival outcomes remains to be further investigated, especially when the target estimand is defined based on the restricted mean survival time (RMST)-a clinically meaningful summary measure free of the proportional hazards assumption. In this article, we combine propensity score weighting and inverse probability of censoring weighting to estimate the restricted mean counterfactual survival times, and propose computationally-efficient variance estimators. We conduct simulations to compare the performance of IPTW, trimming, and OW in terms of bias, variance, and 95% confidence interval coverage, under various degrees of covariate overlap. Regardless of overlap, we demonstrate the advantage of OW over IPTW and trimming methods in bias, variance, and coverage when the estimand is defined based on RMST.

We study the data-generating mechanism for reconstructive SSL to shed light on its effectiveness. With an infinite amount of labeled samples, we provide a sufficient and necessary condition for perfect linear approximation. The condition reveals a full-rank component that preserves the label classes of Y, along with a redundant component. Motivated by the condition, we propose to approximate the redundant component by a low-rank factorization and measure the approximation quality by introducing a new quantity $\epsilon_s$, parameterized by the rank of factorization s. We incorporate $\epsilon_s$ into the excess risk analysis under both linear regression and ridge regression settings, where the latter regularization approach is to handle scenarios when the dimension of the learned features is much larger than the number of labeled samples n for downstream tasks. We design three stylized experiments to compare SSL with supervised learning under different settings to support our theoretical findings.

We study the online learnability of hypothesis classes with respect to arbitrary, but bounded loss functions. No characterization of online learnability is known at this level of generality. We give a new scale-sensitive combinatorial dimension, named the sequential minimax dimension, and show that it gives a tight quantitative characterization of online learnability. In addition, we show that the sequential minimax dimension subsumes most existing combinatorial dimensions in online learning theory.

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the best solutions from the current population and newly-generated solutions (irrespective of the selection criteria used such as Pareto dominance, crowdedness and indicators). In this paper, we question this practice. We analytically present that stochastic population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZeroJump and bi-objective RealRoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed population update method. This work is an attempt to challenge a common practice in the design of existing MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

Face recognition (FR) has reached a high technical maturity. However, its use needs to be carefully assessed from an ethical perspective, especially in sensitive scenarios. This is precisely the focus of this paper: the use of FR for the identification of specific subjects in moderately to densely crowded spaces (e.g. public spaces, sports stadiums, train stations) and law enforcement scenarios. In particular, there is a need to consider the trade-off between the need to protect privacy and fundamental rights of citizens as well as their safety. Recent Artificial Intelligence (AI) policies, notably the European AI Act, propose that such FR interventions should be proportionate and deployed only when strictly necessary. Nevertheless, concrete guidelines on how to address the concept of proportional FR intervention are lacking to date. This paper proposes a framework to contribute to assessing whether an FR intervention is proportionate or not for a given context of use in the above mentioned scenarios. It also identifies the main quantitative and qualitative variables relevant to the FR intervention decision (e.g. number of people in the scene, level of harm that the person(s) in search could perpetrate, consequences to individual rights and freedoms) and propose a 2D graphical model making it possible to balance these variables in terms of ethical cost vs security gain. Finally, different FR scenarios inspired by real-world deployments validate the proposed model. The framework is conceived as a simple support tool for decision makers when confronted with the deployment of an FR system.

The success of deep learning comes at a tremendous computational and energy cost, and the scalability of training massively overparametrized neural networks is becoming a real barrier to the progress of artificial intelligence (AI). Despite the popularity and low cost-per-iteration of traditional backpropagation via gradient decent, stochastic gradient descent (SGD) has prohibitive convergence rate in non-convex settings, both in theory and practice. To mitigate this cost, recent works have proposed to employ alternative (Newton-type) training methods with much faster convergence rate, albeit with higher cost-per-iteration. For a typical neural network with $m=\mathrm{poly}(n)$ parameters and input batch of $n$ datapoints in $\mathbb{R}^d$, the previous work of [Brand, Peng, Song, and Weinstein, ITCS'2021] requires $\sim mnd + n^3$ time per iteration. In this paper, we present a novel training method that requires only $m^{1-\alpha} n d + n^3$ amortized time in the same overparametrized regime, where $\alpha \in (0.01,1)$ is some fixed constant. This method relies on a new and alternative view of neural networks, as a set of binary search trees, where each iteration corresponds to modifying a small subset of the nodes in the tree. We believe this view would have further applications in the design and analysis of deep neural networks (DNNs).

We study inductive bias in Transformers in the infinitely over-parameterized Gaussian process limit and argue transformers tend to be biased towards more permutation symmetric functions in sequence space. We show that the representation theory of the symmetric group can be used to give quantitative analytical predictions when the dataset is symmetric to permutations between tokens. We present a simplified transformer block and solve the model at the limit, including accurate predictions for the learning curves and network outputs. We show that in common setups, one can derive tight bounds in the form of a scaling law for the learnability as a function of the context length. Finally, we argue WikiText dataset, does indeed possess a degree of permutation symmetry.

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