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

Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely affects the performance. We propose a non-classical parameterization for density estimation using the sample moments, which does not require the choice of such functions. The parameterization is induced by the Kullback-Leibler distance, and the solution of it, which is proved to exist and be unique subject to simple prior that does not depend on data, can be obtained by convex optimization. Simulation results show the performance of the proposed estimator in estimating multi-modal densities which are mixtures of different types of functions.

ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction of a model is certifiably robust. Given a learning algorithm that produces a classifier and given an example at test time, a classification outcome is certifiably robust if it is predicted by every model trained across all possible worlds (repairs) of the uncertain (inconsistent) dataset. This notion of robustness falls naturally under the framework of certain answers. In this paper, we study the complexity of certifying robustness for a simple but widely deployed classification algorithm, $k$-Nearest Neighbors ($k$-NN). Our main focus is on inconsistent datasets when the integrity constraints are functional dependencies (FDs). For this setting, we establish a dichotomy in the complexity of certifying robustness w.r.t. the set of FDs: the problem either admits a polynomial time algorithm, or it is coNP-hard. Additionally, we exhibit a similar dichotomy for the counting version of the problem, where the goal is to count the number of possible worlds that predict a certain label. As a byproduct of our study, we also establish the complexity of a problem related to finding an optimal subset repair that may be of independent interest.

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian inference with a Stein discrepancy as a loss function, motivated by applications in which the likelihood contains an intractable normalisation constant. In this context, the Stein discrepancy circumvents evaluation of the normalisation constant and produces generalised posteriors that are either closed form or accessible using standard Markov chain Monte Carlo. On a theoretical level, we show consistency, asymptotic normality, and bias-robustness of the generalised posterior, highlighting how these properties are impacted by the choice of Stein discrepancy. Then, we provide numerical experiments on a range of intractable distributions, including applications to kernel-based exponential family models and non-Gaussian graphical models.

There has recently been a surge of interest in the computational and complexity properties of the population model, which assumes $n$ anonymous, computationally-bounded nodes, interacting at random, and attempting to jointly compute global predicates. Significant work has gone towards investigating majority and consensus dynamics in this model: assuming that each node is initially in one of two states $X$ or $Y$, determine which state had higher initial count. In this paper, we consider a natural generalization of majority/consensus, which we call comparison. We are given two baseline states, $X_0$ and $Y_0$, present in any initial configuration in fixed, possibly small counts. Importantly, one of these states has higher count than the other: we will assume $|X_0| \ge C |Y_0|$ for some constant $C$. The challenge is to design a protocol which can quickly and reliably decide on which of the baseline states $X_0$ and $Y_0$ has higher initial count. We propose a simple algorithm solving comparison: the baseline algorithm uses $O(\log n)$ states per node, and converges in $O(\log n)$ (parallel) time, with high probability, to a state where whole population votes on opinions $X$ or $Y$ at rates proportional to initial $|X_0|$ vs. $|Y_0|$ concentrations. We then describe how such output can be then used to solve comparison. The algorithm is self-stabilizing, in the sense that it converges to the correct decision even if the relative counts of baseline states $X_0$ and $Y_0$ change dynamically during the execution, and leak-robust, in the sense that it can withstand spurious faulty reactions. Our analysis relies on a new martingale concentration result which relates the evolution of a population protocol to its expected (steady-state) analysis, which should be broadly applicable in the context of population protocols and opinion dynamics.

Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to obtain uncertainty estimation or need significant modification (e.g., formulating a proper Bayesian treatment) to obtain it. Most previous methods are not able to take an arbitrary model off the shelf and generate uncertainty estimation without retraining or redesigning it. To address this gap, we perform a systematic exploration into training-free uncertainty estimation for dense regression, an unrecognized yet important problem, and provide a theoretical construction justifying such estimations. We propose three simple and scalable methods to analyze the variance of outputs from a trained network under tolerable perturbations: infer-transformation, infer-noise, and infer-dropout. They operate solely during the inference, without the need to re-train, re-design, or fine-tune the models, as typically required by state-of-the-art uncertainty estimation methods. Surprisingly, even without involving such perturbations in training, our methods produce comparable or even better uncertainty estimation when compared to training-required state-of-the-art methods.

The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that balances expected performance and risk. To the best of our knowledge, PG-BROIL is the first policy optimization algorithm robust to a distribution of reward hypotheses which can scale to continuous MDPs. Results suggest that PG-BROIL can produce a family of behaviors ranging from risk-neutral to risk-averse and outperforms state-of-the-art imitation learning algorithms when learning from ambiguous demonstrations by hedging against uncertainty, rather than seeking to uniquely identify the demonstrator's reward function.

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.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

We propose a new method of estimation in topic models, that is not a variation on the existing simplex finding algorithms, and that estimates the number of topics K from the observed data. We derive new finite sample minimax lower bounds for the estimation of A, as well as new upper bounds for our proposed estimator. We describe the scenarios where our estimator is minimax adaptive. Our finite sample analysis is valid for any number of documents (n), individual document length (N_i), dictionary size (p) and number of topics (K), and both p and K are allowed to increase with n, a situation not handled well by previous analyses. We complement our theoretical results with a detailed simulation study. We illustrate that the new algorithm is faster and more accurate than the current ones, although we start out with a computational and theoretical disadvantage of not knowing the correct number of topics K, while we provide the competing methods with the correct value in our simulations.

From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is more robust against overfitting, and thus we are able to use very flexible models (such as deep neural networks) given limited P data. Moreover, we analyze the bias, consistency, and mean-squared-error reduction of the proposed risk estimator, and bound the estimation error of the resulting empirical risk minimizer. Experiments demonstrate that our risk estimator fixes the overfitting problem of its unbiased counterparts.