Backdoor attacks involve the injection of a limited quantity of poisoned examples containing triggers into the training dataset. During the inference stage, backdoor attacks can uphold a high level of accuracy for normal examples, yet when presented with trigger-containing instances, the model may erroneously predict them as the targeted class designated by the attacker. This paper explores strategies for mitigating the risks associated with backdoor attacks by examining the filtration of poisoned samples.We primarily leverage two key characteristics of backdoor attacks: the ability for multiple backdoors to exist simultaneously within a single model, and the discovery through Composite Backdoor Attack (CBA) that altering two triggers in a sample to new target labels does not compromise the original functionality of the triggers, yet enables the prediction of the data as a new target class when both triggers are present simultaneously.Therefore, a novel three-stage poisoning data filtering approach, known as Composite Backdoor Poison Filtering (CBPF), is proposed as an effective solution. Firstly, utilizing the identified distinctions in output between poisoned and clean samples, a subset of data is partitioned to include both poisoned and clean instances. Subsequently, benign triggers are incorporated and labels are adjusted to create new target and benign target classes, thereby prompting the poisoned and clean data to be classified as distinct entities during the inference stage. The experimental results indicate that CBPF is successful in filtering out malicious data produced by six advanced attacks on CIFAR10 and ImageNet-12. On average, CBPF attains a notable filtering success rate of 99.91% for the six attacks on CIFAR10. Additionally, the model trained on the uncontaminated samples exhibits sustained high accuracy levels.

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In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed Monte Carlo (CMC) scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing.