亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

Bayesian nonparametric hierarchical priors provide flexible models for sharing of information within and across groups. We focus on latent feature allocation models, where the data structures correspond to multisets or unbounded sparse matrices. The fundamental development in this regard is the Hierarchical Indian Buffet process (HIBP), devised by Thibaux and Jordan (2007). However, little is known in terms of explicit tractable descriptions of the joint, marginal, posterior and predictive distributions of the HIBP. We provide explicit novel descriptions of these quantities, in the Bernoulli HIBP and general spike and slab HIBP settings, which allows for exact sampling and simpler practical implementation. We then extend these results to the more complex setting of hierarchies of general HIBP (HHIBP). The generality of our framework allows one to recognize important structure that may otherwise be masked in the Bernoulli setting, and involves characterizations via dynamic mixed Poisson random count matrices. Our analysis shows that the standard choice of hierarchical Beta processes for modeling across group sharing is not ideal in the classic Bernoulli HIBP setting proposed by Thibaux and Jordan (2007), or other spike and slab HIBP settings, and we thus indicate tractable alternative priors.

Dirty Paper Coding (DPC) is considered as the optimal precoding which achieves capacity for the Gaussian Multiple-Input Multiple-Output (MIMO) broadcast channel (BC). However, to find the optimal precoding order, it needs to repeat N! times for N users as there are N! possible precoding orders. This extremely high complexity limits its practical use in modern wireless networks. In this paper, we show the equivalence of DPC and the recently proposed Higher Order Mercer's Theorem (HOGMT) precoding[1][2] in 2-D (spatial) case, which provides an alternate implementation for DPC. Furthermore, we show that the proposed implementation method is linear over the permutation operator when permuting over multi-user channels. Therefore, we present a low complexity algorithm that optimizes the precoding order for DPC with beamforming, eliminating repeated computation of DPC for each precoding order. Simulations show that our method can achieve the same result as conventional DPC with about 20 dB lower complexity for N = 5 users.

Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of $O(\frac{ds}{n\epsilon^2})$, where $d$ represents the dimension of the numerical vector and $s$ denotes the number of non-zero entries. By converting the conditional/unconditional numerical mean estimation problem into a frequency estimation problem, we develop an optimal and efficient mechanism called Collision. In contrast, existing methods exhibit sub-optimal error rates of $O(\frac{d^2}{n\epsilon^2})$ or $O(\frac{ds^2}{n\epsilon^2})$. Specifically, for unconditional mean estimation, we leverage the negative correlation between two frequencies in each dimension and propose the CoCo mechanism, which further reduces estimation errors for mean values compared to Collision. Moreover, to surpass the error barrier in local privacy, we examine privacy amplification in the shuffle model for the proposed mechanisms and derive precisely tight amplification bounds. Our experiments validate and compare our mechanisms with existing approaches, demonstrating significant error reductions for frequency estimation and mean estimation on numerical vectors.

Proximal causal inference is a recently proposed framework for evaluating the causal effect of a treatment on an outcome variable in the presence of unmeasured confounding (Miao et al., 2018a; Tchetgen Tchetgen et al., 2020). For nonparametric point identification, the framework leverages proxy variables of unobserved confounders, provided that such proxies are sufficiently relevant for the latter, a requirement that has previously been formalized as a completeness condition. Completeness is key to connecting the observed proxy data to hidden factors via a so-called confounding bridge function, identification of which is an important step towards proxy-based point identification of causal effects. However, completeness is well-known not to be empirically testable, therefore potentially restricting the application of the proximal causal framework. In this paper, we propose partial identification methods that do not require completeness and obviate the need for identification of a bridge function. That is, we establish that proxies of unobserved confounders can be leveraged to obtain bounds on the causal effect of the treatment on the outcome even if available information does not suffice to identify either a bridge function or a corresponding causal effect of interest. We further establish analogous partial identification results in related settings where identification hinges upon hidden mediators for which proxies are available, however such proxies are not sufficiently rich for point identification of a bridge function or a corresponding causal effect of interest.

To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial.

Making causal inferences from observational studies can be challenging when confounders are missing not at random. In such cases, identifying causal effects is often not guaranteed. Motivated by a real example, we consider a treatment-independent missingness assumption under which we establish the identification of causal effects when confounders are missing not at random. We propose a weighted estimating equation (WEE) approach for estimating model parameters and introduce three estimators for the average causal effect, based on regression, propensity score weighting, and doubly robust estimation. We evaluate the performance of these estimators through simulations, and provide a real data analysis to illustrate our proposed method.

This paper presents an approximate wireless communication scheme for federated learning (FL) model aggregation in the uplink transmission. We consider a realistic channel that reveals bit errors during FL model exchange in wireless networks. Our study demonstrates that random bit errors during model transmission can significantly affect FL performance. To overcome this challenge, we propose an approximate communication scheme based on the mathematical and statistical proof that machine learning (ML) model gradients are bounded under certain constraints. This bound enables us to introduce a novel encoding scheme for float-to-binary representation of gradient values and their QAM constellation mapping. Besides, since FL gradients are error-resilient, the proposed scheme simply delivers gradients with errors when the channel quality is satisfactory, eliminating extensive error-correcting codes and/or retransmission. The direct benefits include less overhead and lower latency. The proposed scheme is well-suited for resource-constrained devices in wireless networks. Through simulations, we show that the proposed scheme is effective in reducing the impact of bit errors on FL performance and saves at least half the time than transmission with error correction and retransmission to achieve the same learning performance. In addition, we investigated the effectiveness of bit protection mechanisms in high-order modulation when gray coding is employed and found that this approach considerably enhances learning performance.

Effective multi-robot teams require the ability to move to goals in complex environments in order to address real-world applications such as search and rescue. Multi-robot teams should be able to operate in a completely decentralized manner, with individual robot team members being capable of acting without explicit communication between neighbors. In this paper, we propose a novel game theoretic model that enables decentralized and communication-free navigation to a goal position. Robots each play their own distributed game by estimating the behavior of their local teammates in order to identify behaviors that move them in the direction of the goal, while also avoiding obstacles and maintaining team cohesion without collisions. We prove theoretically that generated actions approach a Nash equilibrium, which also corresponds to an optimal strategy identified for each robot. We show through extensive simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, and is able to avoid obstacles and collisions, maintain connectivity, and respond robustly to sensor noise.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.