Categorization is a significant task in decision-making, which is a key part of human behavior. An interference effect is caused by categorization in some cases, which breaks the total probability principle. A negation quantum model (NQ model) is developed in this article to predict the interference. Taking the advantage of negation to bring more information in the distribution from a different perspective, the proposed model is a combination of the negation of a probability distribution and the quantum decision model. Information of the phase contained in quantum probability and the special calculation method to it can easily represented the interference effect. The results of the proposed NQ model is closely to the real experiment data and has less error than the existed models.

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully probabilistic models aim at modeling the data distribution directly. Consequently, they provide functionalities that are highly relevant for continual learning, such as density estimation (outlier detection) and sample generation. As a concrete realization of generative continual learning, we propose Gaussian Mixture Replay (GMR). GMR is a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. Relying on the MNIST, FashionMNIST and Devanagari benchmarks, we first demonstrate unsupervised task boundary detection by GMM density estimation, which we also use to reject untypical generated samples. In addition, we show that GMR is capable of class-conditional sampling in the way of a cGAN. Lastly, we verify that GMR, despite its simple structure, achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well explored for classical Bayesian Statistics, it appears useful to develop a corresponding method for complex Machine Learning problems. Given their underlying Bayesian framework and their widespread popularity, Gaussian Processes are a good candidate to tackle this task. We therefore extend the idea of Mixture models for Gaussian Process regression in order to work with multiple prior beliefs at once - both a analytical regression formula and a Sparse Variational approach are considered. In addition, we consider the usage of our approach to additionally account for the problem of prior misspecification in functional regression problems.

Network Intrusion Detection Systems (NIDSs) are an increasingly important tool for the prevention and mitigation of cyber attacks. A number of labelled synthetic datasets generated have been generated and made publicly available by researchers, and they have become the benchmarks via which new ML-based NIDS classifiers are being evaluated. Recently published results show excellent classification performance with these datasets, increasingly approaching 100 percent performance across key evaluation metrics such as accuracy, F1 score, etc. Unfortunately, we have not yet seen these excellent academic research results translated into practical NIDS systems with such near-perfect performance. This motivated our research presented in this paper, where we analyse the statistical properties of the benign traffic in three of the more recent and relevant NIDS datasets, (CIC, UNSW, ...). As a comparison, we consider two datasets obtained from real-world production networks, one from a university network and one from a medium size Internet Service Provider (ISP). Our results show that the two real-world datasets are quite similar among themselves in regards to most of the considered statistical features. Equally, the three synthetic datasets are also relatively similar within their group. However, and most importantly, our results show a distinct difference of most of the considered statistical features between the three synthetic datasets and the two real-world datasets. Since ML relies on the basic assumption of training and test datasets being sampled from the same distribution, this raises the question of how well the performance results of ML-classifiers trained on the considered synthetic datasets can translate and generalise to real-world networks. We believe this is an interesting and relevant question which provides motivation for further research in this space.

Topic models have been successfully used for analyzing text documents. However, with existing topic models, many documents are required for training. In this paper, we propose a neural network-based few-shot learning method that can learn a topic model from just a few documents. The neural networks in our model take a small number of documents as inputs, and output topic model priors. The proposed method trains the neural networks such that the expected test likelihood is improved when topic model parameters are estimated by maximizing the posterior probability using the priors based on the EM algorithm. Since each step in the EM algorithm is differentiable, the proposed method can backpropagate the loss through the EM algorithm to train the neural networks. The expected test likelihood is maximized by a stochastic gradient descent method using a set of multiple text corpora with an episodic training framework. In our experiments, we demonstrate that the proposed method achieves better perplexity than existing methods using three real-world text document sets.

Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several approaches have been proposed to overcome this issue, from non-parametric schemes that aggregate states or actions to parametric approximations of state and action VFs via, e.g., linear estimators or deep neural networks. Relevantly, several high-dimensional state problems can be well-approximated by an intrinsic low-rank structure. Motivated by this and leveraging results from low-rank optimization, this paper proposes different stochastic algorithms to estimate a low-rank factorization of the $Q(s, a)$ matrix. This is a non-parametric alternative to VF approximation that dramatically reduces the computational and sample complexities relative to classical $Q$-learning methods that estimate $Q(s,a)$ separately for each state-action pair.

We introduce distributed NLI, a new NLU task with a goal to predict the distribution of human judgements for natural language inference. We show that models can capture human judgement distribution by applying additional distribution estimation methods, namely, Monte Carlo (MC) Dropout, Deep Ensemble, Re-Calibration, and Distribution Distillation. All four of these methods substantially outperform the softmax baseline. We show that MC Dropout is able to achieve decent performance without any distribution annotations while Re-Calibration can further give substantial improvements when extra distribution annotations are provided, suggesting the value of multiple annotations for the example in modeling the distribution of human judgements. Moreover, MC Dropout and Re-Calibration can achieve decent transfer performance on out-of-domain data. Despite these improvements, the best results are still far below estimated human upper-bound, indicating that the task of predicting the distribution of human judgements is still an open, challenging problem with large room for future improvements. We showcase the common errors for MC Dropout and Re-Calibration. Finally, we give guidelines on the usage of these methods with different levels of data availability and encourage future work on modeling the human opinion distribution for language reasoning.

$\alpha$-posteriors and their variational approximations distort standard posterior inference by downweighting the likelihood and introducing variational approximation errors. We show that such distortions, if tuned appropriately, reduce the Kullback-Leibler (KL) divergence from the true, but perhaps infeasible, posterior distribution when there is potential parametric model misspecification. To make this point, we derive a Bernstein-von Mises theorem showing convergence in total variation distance of $\alpha$-posteriors and their variational approximations to limiting Gaussian distributions. We use these distributions to evaluate the KL divergence between true and reported posteriors. We show this divergence is minimized by choosing $\alpha$ strictly smaller than one, assuming there is a vanishingly small probability of model misspecification. The optimized value becomes smaller as the the misspecification becomes more severe. The optimized KL divergence increases logarithmically in the degree of misspecification and not linearly as with the usual posterior.

Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world data creates the need to rely on synthetic data for the evaluation of these methods. Existing benchmarks are limited in their scope, as they either are restricted to a "static" selection of data sets, or do not allow for a granular assessment of the methods' performance when commonly made assumptions are violated. We propose a flexible and simple to use framework for generating time series data, which is aimed at developing, evaluating, and benchmarking time series causal discovery methods. In particular, the framework can be used to fine tune novel methods on vast amounts of data, without "overfitting" them to a benchmark, but rather so they perform well in real-world use cases. Using our framework, we evaluate prominent time series causal discovery methods and demonstrate a notable degradation in performance when their assumptions are invalidated and their sensitivity to choice of hyperparameters. Finally, we propose future research directions and how our framework can support both researchers and practitioners.

Hawkes processes are a popular means of modeling the event times of self-exciting phenomena, such as earthquake strikes or tweets on a topical subject. Classically, these models are fit to historical event time data via likelihood maximization. However, in many scenarios, the exact times of historical events are not recorded for either privacy (e.g., patient admittance to hospitals) or technical limitations (e.g., most transport data records the volume of vehicles passing loop detectors but not the individual times). The interval-censored setting denotes when only the aggregate counts of events at specific time intervals are observed. Fitting the parameters of interval-censored Hawkes processes requires designing new training objectives that do not rely on the exact event times. In this paper, we propose a model to estimate the parameters of a Hawkes process in interval-censored settings. Our model builds upon the existing Hawkes Intensity Process (HIP) of in several important directions. First, we observe that while HIP is formulated in terms of expected intensities, it is more natural to work instead with expected counts; further, one can express the latter as the solution to an integral equation closely related to the defining equation of HIP. Second, we show how a non-homogeneous Poisson approximation to the Hawkes process admits a tractable likelihood in the interval-censored setting; this approximation recovers the original HIP objective as a special case, and allows for the use of a broader class of Bregman divergences as loss function. Third, we explicate how to compute a tighter approximation to the ground truth in the likelihood. Finally, we show how our model can incorporate information about varying interval lengths. Experiments on synthetic and real-world data confirm our HIPPer model outperforms HIP and several other baselines on the task of interval-censored inference.