搜索结果：Rejection

We study an OTC FX market-making problem, built on the Avellaneda-Stoikov tradition, in which a dealer streams size-dependent quotes on a discrete ladder and manages inventory risk over a finite horizon under Poisson arrivals of trade requests. Adverse selection is modelled through latency-driven price moves over a delay window, represented by Gaussian marks whose conditional means can depend on the quoted spread, capturing selective client reaction to stale quotes. The dealer can address latency risk through trade rejection when slippage breaches a tolerance threshold. We treat slippage tolerance as an explicit control jointly optimized with quotes: upon receiving a trade request, the dealer chooses an acceptance/rejection rule, which makes the trade economically akin to an embedded option written on the latency price move. We further introduce rejection feedback through an EMA-based rejection score used as a reputation proxy, so that client intensity is endogenously modulated by past rejections via a multiplicative factor. Using dynamic programming, we derive a Markov control problem with state variables (inventory, rejection-score) and show how rejection decision enters the HJB

Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without performance guarantees. In this paper, we present pliable rejection sampling (PRS), a new approach to rejection sampling, where we learn the sampling proposal using a kernel estimator. Since our method builds on rejection sampling, the samples obtained are with high probability i.i.d. and distributed according to f. Moreover, PRS comes with a guarantee on the number of accepted samples.

Recently, there is an emerging interest in adversarially training a classifier with a rejection option (also known as a selective classifier) for boosting adversarial robustness. While rejection can incur a cost in many applications, existing studies typically associate zero cost with rejecting perturbed inputs, which can result in the rejection of numerous slightly-perturbed inputs that could be correctly classified. In this work, we study adversarially-robust classification with rejection in the stratified rejection setting, where the rejection cost is modeled by rejection loss functions monotonically non-increasing in the perturbation magnitude. We theoretically analyze the stratified rejection setting and propose a novel defense method -- Adversarial Training with Consistent Prediction-based Rejection (CPR) -- for building a robust selective classifier. Experiments on image datasets demonstrate that the proposed method significantly outperforms existing methods under strong adaptive attacks. For instance, on CIFAR-10, CPR reduces the total robust loss (for different rejection losses) by at least 7.3% under both seen and unseen attacks.

This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process whose stationary distribution coincides with a target density known only up to a normalizing constant. Unlike standard Rejection Sampling, RRS does not require the existence of a finite constant that upper-bounds the likelihood ratio. As a result, its total variation convergence rate remains exponential for a larger class of scenarios compared to, for example, the Independent Metropolis-Hastings sampler, which requires a finite bounding constant. To explain the workings of the method, we first present a detailed review of renewal and regenerative processes, including their limit theorems, stationary versions, and convergence properties under standard conditions. We explain a coupling proof for exponential convergence of regenerative processes, under the assumption of a spread-out cycle length distribution. We then introduce the RRS algorithm, and derive its convergence rate. Its performance is compared theoretically and empirically with classical

Overconfidence in deep learning models poses a significant risk in high-stakes medical imaging tasks, particularly in multi-label classification of chest X-rays, where multiple co-occurring pathologies must be detected simultaneously. This study introduces an uncertainty-aware framework for chest X-ray diagnosis based on a DenseNet-121 backbone, enhanced with two selective prediction mechanisms: entropy-based rejection and confidence interval-based rejection. Both methods enable the model to abstain from uncertain predictions, improving reliability by deferring ambiguous cases to clinical experts. A quantile-based calibration procedure is employed to tune rejection thresholds using either global or class-specific strategies. Experiments conducted on three large public datasets (PadChest, NIH ChestX-ray14, and MIMIC-CXR) demonstrate that selective rejection improves the trade-off between diagnostic accuracy and coverage, with entropy-based rejection yielding the highest average AUC across all pathologies. These results support the integration of selective prediction into AI-assisted diagnostic workflows, providing a practical step toward safer, uncertainty-aware deployment of deep l

Variational Inference (VI) is a fundamental inference technique in Bayesian machine learning for approximating complex posterior distributions. Traditional VI often relies on the mean-field factorization, which can inadequately capture true posterior complexity. Recent advancements have leveraged neural networks to model implicit distributions, offering increased flexibility. However, the practical constraints of neural network architectures still produces inaccuracies. In this paper, we propose a method called Implicit Variational Rejection Sampling (IVRS), which integrates implicit distributions with rejection sampling to improve the posterior approximation. Our method uses neural networks to construct implicit proposal distributions, and rejection sampling with a discriminator network that estimates the density ratio between the implicit proposal and the true posterior for refining the approximation. Towards this end, we introduce the Implicit Resampling Evidence Lower Bound (IR-ELBO) as a metric to characterize the resampled distribution's quality and derive a tighter variational lower bound. Experimental results demonstrate that our method outperforms traditional variational i

Learning with rejection is an important framework that can refrain from making predictions to avoid critical mispredictions by balancing between prediction and rejection. Previous studies on cost-based rejection only focused on the classification setting, which cannot handle the continuous and infinite target space in the regression setting. In this paper, we investigate a novel regression problem called regression with cost-based rejection, where the model can reject to make predictions on some examples given certain rejection costs. To solve this problem, we first formulate the expected risk for this problem and then derive the Bayes optimal solution, which shows that the optimal model should reject to make predictions on the examples whose variance is larger than the rejection cost when the mean squared error is used as the evaluation metric. Furthermore, we propose to train the model by a surrogate loss function that considers rejection as binary classification and we provide conditions for the model consistency, which implies that the Bayes optimal solution can be recovered by our proposed surrogate loss. Extensive experiments demonstrate the effectiveness of our proposed meth

Solid organ transplantation has by now become a common medical procedure. Owing to the introduction of new immunosuppressive drugs, the allograft loss due to acute rejection has been reduced significantly over time. Tragically, the number of donor organs lost due to allograft vasculopathy (AV), generally named chronic vascular rejection or chronic rejection, has remained significant and unchanged for decades. We argue that designation of AV as chronic rejection, and its classification as a delayed long-lasting reaction of recipient immune effectors against donor alloantigens have given us the wrong impression that we have identified the necessary cause of the disease. However, whatever treatment options we have in the anti-rejection toolbox, despite their success in treating acute rejection, do not work for AV. Yet, the scientific community has continued to conceptualize and approach AV within the alloimmunity and rejection model. Due to unproductive research from the alloimmunity perspective, the number of transplanted hearts lost due to this pathology today is almost the same as it was fifty years ago. We believe that this phenomenon falls under the rubric of linguistic relativit

In this paper, we propose an optimal rejection method for rejecting ambiguous samples by a rejection function. This rejection function is trained together with a classification function under the framework of Learning-with-Rejection (LwR). The highlights of LwR are: (1) the rejection strategy is not heuristic but has a strong background from a machine learning theory, and (2) the rejection function can be trained on an arbitrary feature space which is different from the feature space for classification. The latter suggests we can choose a feature space that is more suitable for rejection. Although the past research on LwR focused only on its theoretical aspect, we propose to utilize LwR for practical pattern classification tasks. Moreover, we propose to use features from different CNN layers for classification and rejection. Our extensive experiments of notMNIST classification and character/non-character classification demonstrate that the proposed method achieves better performance than traditional rejection strategies.

The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds. It can be used to sample from any probability density which ``depends only on distance". The idea is to combine the statistical principle of rejection sampling with the geometric principle of volume comparison. CURS is an exact sampling method and (assuming the underlying Riemannian manifold satisfies certain technical conditions) it has a particularly moderate computational cost. The aim of the present work is to show that there are many applications where CURS should be the user's method of choice for dealing with relatively low-dimensional scenarios.

Diabetic retinopathy (DR) is a major cause of visual impairment, and effective treatment options depend heavily on timely and accurate diagnosis. Deep learning models have demonstrated great success identifying DR from retinal images. However, relying only on predictions made by models, without any indication of model confidence, creates uncertainty and poses significant risk in clinical settings. This paper investigates an alternative in uncertainty-aware deep learning models, including a rejection mechanism to reject low-confidence predictions, contextualized by deferred decision-making in clinical practice. The results show there is a trade-off between prediction coverage and coverage reliability. The Variational Bayesian model adopted a more conservative strategy when predicting DR, subsequently rejecting the uncertain predictions. The model is evaluated by means of important performance metrics such as Accuracy on accepted predictions, the proportion of accepted cases (coverage), the rejection-ratio, and Expected Calibration Error (ECE). The findings also demonstrate a clear trade-off between accuracy and caution, establishing that the use of uncertainty estimation and selecti

Motivated by green manufacturing, this paper investigates a scheduling with rejection problem subject to an energy consumption constraint. Machines are associated with non-uniform energy consumption rates, defined as the energy consumed per unit time. Each job is either rejected with a rejection penalty or accepted and scheduled on some machine for processing, which incurs energy consumption. The problem aims to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs while the total energy consumption is bounded by a given threshold. In this paper, when the number of machines is part of the input, we develop the first $(2+ε)$-approximation algorithm for any fixed constant $ε$ and a simple QPTAS as well as a PTAS for uniform energy consumption rates. Moreover, we present an FPTAS when the number of machines is a fixed constant.

Anomaly detection aims at detecting unexpected behaviours in the data. Because anomaly detection is usually an unsupervised task, traditional anomaly detectors learn a decision boundary by employing heuristics based on intuitions, which are hard to verify in practice. This introduces some uncertainty, especially close to the decision boundary, that may reduce the user trust in the detector's predictions. A way to combat this is by allowing the detector to reject examples with high uncertainty (Learning to Reject). This requires employing a confidence metric that captures the distance to the decision boundary and setting a rejection threshold to reject low-confidence predictions. However, selecting a proper metric and setting the rejection threshold without labels are challenging tasks. In this paper, we solve these challenges by setting a constant rejection threshold on the stability metric computed by ExCeeD. Our insight relies on a theoretical analysis of such a metric. Moreover, setting a constant threshold results in strong guarantees: we estimate the test rejection rate, and derive a theoretical upper bound for both the rejection rate and the expected prediction cost. Experime

Asymptotic disturbance rejection (equivalently tracking) for nonlinear systems has been studied only in qualitative terms (the state is asymptotically stable under bounded disturbances). We show how to prove quantitative performance guarantees for the nonlinear servomechanism problem. Our technique originates by applying a gain inequalities point of view to an ad fontes reexamination of the linear problem: what is the nonlinear equivalent of a sensitivity transfer function with a zero at the origin? We answer: a nonlinear input-output system is high-pass if its output is stable with respect to the \emph{derivative} of the input. We first show that definition generalizes high-pass resistor-capacitor circuit analysis to accommodate nonlinear resistors. We then show that this definition generalizes the steady-state disturbance rejection property of integral feedback controllers for linear systems. The theoretical payoff is that low-frequency disturbance rejection is captured by a quantitative, non-asymptotic output cost bound. Finally, we raise theoretical questions about compositionality of nonlinear operators.

Classification with rejection emerges as a learning paradigm which allows models to abstain from making predictions. The predominant approach is to alter the supervised learning pipeline by augmenting typical loss functions, letting model rejection incur a lower loss than an incorrect prediction. Instead, we propose a different distributional perspective, where we seek to find an idealized data distribution which maximizes a pretrained model's performance. This can be formalized via the optimization of a loss's risk with a $\varphi$-divergence regularization term. Through this idealized distribution, a rejection decision can be made by utilizing the density ratio between this distribution and the data distribution. We focus on the setting where our $\varphi$-divergences are specified by the family of $α$-divergence. Our framework is tested empirically over clean and noisy datasets.

Learning with rejection has been a prototypical model for studying the human-AI interaction on prediction tasks. Upon the arrival of a sample instance, the model first uses a rejector to decide whether to accept and use the AI predictor to make a prediction or reject and defer the sample to humans. Learning such a model changes the structure of the original loss function and often results in undesirable non-convexity and inconsistency issues. For the classification with rejection problem, several works develop consistent surrogate losses for the joint learning of the predictor and the rejector, while there have been fewer works for the regression counterpart. This paper studies the regression with rejection (RwR) problem and investigates a no-rejection learning strategy that uses all the data to learn the predictor. We first establish the consistency for such a strategy under the weak realizability condition. Then for the case without the weak realizability, we show that the excessive risk can also be upper bounded with the sum of two parts: prediction error and calibration error. Lastly, we demonstrate the advantage of such a proposed learning strategy with empirical evidence.

Recent advances in powerful pre-trained diffusion models encourage the development of methods to improve the sampling performance under well-trained diffusion models. This paper introduces Diffusion Rejection Sampling (DiffRS), which uses a rejection sampling scheme that aligns the sampling transition kernels with the true ones at each timestep. The proposed method can be viewed as a mechanism that evaluates the quality of samples at each intermediate timestep and refines them with varying effort depending on the sample. Theoretical analysis shows that DiffRS can achieve a tighter bound on sampling error compared to pre-trained models. Empirical results demonstrate the state-of-the-art performance of DiffRS on the benchmark datasets and the effectiveness of DiffRS for fast diffusion samplers and large-scale text-to-image diffusion models. Our code is available at https://github.com/aailabkaist/DiffRS.

A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be nontrivial and can involve an intractable normalizing constant. Rejection sampling may be used to generate exact draws, but requires formulation of a suitable proposal distribution. To be practically useful, the proposal must both be convenient to sample from and not reject candidate draws too frequently. A well-known approach to design a proposal involves decomposing the target density into a finite mixture, whose components may correspond to a partition of the support. This work considers such a construction that focuses on majorization of the weight function. This approach may be applicable when assumptions for adaptive rejection sampling and related algorithms are not met. An upper bound for the rejection probability based on this construction can be expressed to evaluate the efficiency of the proposal before sampling. A method to partition the support is considered where regions are bifurcated based on their contribution to the bound. Several appl

Rejection sampling methods have recently been proposed to improve the performance of discriminator-based generative models. However, these methods are only optimal under an unlimited sampling budget, and are usually applied to a generator trained independently of the rejection procedure. We first propose an Optimal Budgeted Rejection Sampling (OBRS) scheme that is provably optimal with respect to \textit{any} $f$-divergence between the true distribution and the post-rejection distribution, for a given sampling budget. Second, we propose an end-to-end method that incorporates the sampling scheme into the training procedure to further enhance the model's overall performance. Through experiments and supporting theory, we show that the proposed methods are effective in significantly improving the quality and diversity of the samples.