This paper proposes an extension of regression trees by quadratic unconstrained binary optimization (QUBO). Regression trees are very popular prediction models that are trainable with tabular datasets, but their accuracy is insufficient because the decision rules are too simple. The proposed method extends the decision rules in decision trees to multi-dimensional boundaries. Such an extension is generally unimplementable because of computational limitations, however, the proposed method transforms the training process to QUBO, which enables an annealing machine to solve this problem.

The recent explosion of genetic and high dimensional biobank and 'omic' data has provided researchers with the opportunity to investigate the shared genetic origin (pleiotropy) of hundreds to thousands of related phenotypes. However, existing methods for multi-phenotype genome-wide association studies (GWAS) do not model pleiotropy, are only applicable to a small number of phenotypes, or provide no way to perform inference. To add further complication, raw genetic and phenotype data are rarely observed, meaning analyses must be performed on GWAS summary statistics whose statistical properties in high dimensions are poorly understood. We therefore developed a novel model, theoretical framework, and set of methods to perform Bayesian inference in GWAS of high dimensional phenotypes using summary statistics that explicitly model pleiotropy, beget fast computation, and facilitate the use of biologically informed priors. We demonstrate the utility of our procedure by applying it to metabolite GWAS, where we develop new nonparametric priors for genetic effects on metabolite levels that use known metabolic pathway information and foster interpretable inference at the pathway level.

The Wasserstein distance between mixing measures has come to occupy a central place in the statistical analysis of mixture models. This work proposes a new canonical interpretation of this distance and provides tools to perform inference on the Wasserstein distance between mixing measures in topic models. We consider the general setting of an identifiable mixture model consisting of mixtures of distributions from a set $\mathcal{A}$ equipped with an arbitrary metric $d$, and show that the Wasserstein distance between mixing measures is uniquely characterized as the most discriminative convex extension of the metric $d$ to the set of mixtures of elements of $\mathcal{A}$. The Wasserstein distance between mixing measures has been widely used in the study of such models, but without axiomatic justification. Our results establish this metric to be a canonical choice. Specializing our results to topic models, we consider estimation and inference of this distance. Though upper bounds for its estimation have been recently established elsewhere, we prove the first minimax lower bounds for the estimation of the Wasserstein distance in topic models. We also establish fully data-driven inferential tools for the Wasserstein distance in the topic model context. Our results apply to potentially sparse mixtures of high-dimensional discrete probability distributions. These results allow us to obtain the first asymptotically valid confidence intervals for the Wasserstein distance in topic models.

The issue of distinguishing between the same-source and different-source hypotheses based on various types of traces is a generic problem in forensic science. This problem is often tackled with Bayesian approaches, which are able to provide a likelihood ratio that quantifies the relative strengths of evidence supporting each of the two competing hypotheses. Here, we focus on distance-based approaches, whose robustness and specifically whose capacity to deal with high-dimensional evidence are very different, and need to be evaluated and optimized. A unified framework for direct methods based on estimating the likelihoods of the distance between traces under each of the two competing hypotheses, and indirect methods using logistic regression to discriminate between same-source and different-source distance distributions, is presented. Whilst direct methods are more flexible, indirect methods are more robust and quite natural in machine learning. Moreover, indirect methods also enable the use of a vectorial distance, thus preventing the severe information loss suffered by scalar distance approaches.Direct and indirect methods are compared in terms of sensitivity, specificity and robustness, with and without dimensionality reduction, with and without feature selection, on the example of hand odor profiles, a novel and challenging type of evidence in the field of forensics. Empirical evaluations on a large panel of 534 subjects and their 1690 odor traces show the significant superiority of the indirect methods, especially without dimensionality reduction, be it with or without feature selection.

Concept bottleneck model (CBM) is a ubiquitous method that can interpret neural networks using concepts. In CBM, concepts are inserted between the output layer and the last intermediate layer as observable values. This helps in understanding the reason behind the outputs generated by the neural networks: the weights corresponding to the concepts from the last hidden layer to the output layer. However, it has not yet been possible to understand the behavior of the generalization error in CBM since a neural network is a singular statistical model in general. When the model is singular, a one to one map from the parameters to probability distributions cannot be created. This non-identifiability makes it difficult to analyze the generalization performance. In this study, we mathematically clarify the Bayesian generalization error and free energy of CBM when its architecture is three-layered linear neural networks. We also consider a multitask problem where the neural network outputs not only the original output but also the concepts. The results show that CBM drastically changes the behavior of the parameter region and the Bayesian generalization error in three-layered linear neural networks as compared with the standard version, whereas the multitask formulation does not.

The label distribution skew induced data heterogeniety has been shown to be a significant obstacle that limits the model performance in federated learning, which is particularly developed for collaborative model training over decentralized data sources while preserving user privacy. This challenge could be more serious when the participating clients are in unstable circumstances and dropout frequently. Previous work and our empirical observations demonstrate that the classifier head for classification task is more sensitive to label skew and the unstable performance of FedAvg mainly lies in the imbalanced training samples across different classes. The biased classifier head will also impact the learning of feature representations. Therefore, maintaining a balanced classifier head is of significant importance for building a better global model. To this end, we propose a simple yet effective framework by introducing a prior-calibrated softmax function for computing the cross-entropy loss and a prototype-based feature augmentation scheme to re-balance the local training, which are lightweight for edge devices and can facilitate the global model aggregation. The improved model performance over existing baselines in the presence of non-IID data and client dropout is demonstrated by conducting extensive experiments on benchmark classification tasks.

Today, people use email services such as Gmail, Outlook, AOL Mail, etc. to communicate with each other as quickly as possible to send information and official letters. Spam or junk mail is a major challenge to this type of communication, usually sent by botnets with the aim of advertising, harming and stealing information in bulk to different people. Receiving unwanted spam emails on a daily basis fills up the inbox folder. Therefore, spam detection is a fundamental challenge, so far many works have been done to detect spam using clustering and text categorisation methods. In this article, the author has used the spaCy natural language processing library and 3 machine learning (ML) algorithms Naive Bayes (NB), Decision Tree C45 and Multilayer Perceptron (MLP) in the Python programming language to detect spam emails collected from the Gmail service. Observations show the accuracy rate (96%) of the Multilayer Perceptron (MLP) algorithm in spam detection.

Deep neural retrieval models have amply demonstrated their power but estimating the reliability of their predictions remains challenging. Most dialog response retrieval models output a single score for a response on how relevant it is to a given question. However, the bad calibration of deep neural network results in various uncertainty for the single score such that the unreliable predictions always misinform user decisions. To investigate these issues, we present an efficient calibration and uncertainty estimation framework PG-DRR for dialog response retrieval models which adds a Gaussian Process layer to a deterministic deep neural network and recovers conjugacy for tractable posterior inference by P\'{o}lya-Gamma augmentation. Finally, PG-DRR achieves the lowest empirical calibration error (ECE) in the in-domain datasets and the distributional shift task while keeping $R_{10}@1$ and MAP performance.

This paper gives a simple theory of inference to logically reason symbolic knowledge fully from data over time. We take a Bayesian approach to model how data causes symbolic knowledge. Probabilistic reasoning with symbolic knowledge is modelled as a process of going the causality forwards and backwards. The forward and backward processes correspond to an interpretation and inverse interpretation of formal logic, respectively. The theory is applied to a localisation problem to show a robot with broken or noisy sensors can efficiently solve the problem in a fully data-driven fashion.

Many real-world systems are described not only by data from a single source but via multiple data views. In genomic medicine, for instance, patients can be characterized by data from different molecular layers. Latent variable models with structured sparsity are a commonly used tool for disentangling variation within and across data views. However, their interpretability is cumbersome since it requires a direct inspection and interpretation of each factor from domain experts. Here, we propose MuVI, a novel multi-view latent variable model based on a modified horseshoe prior for modeling structured sparsity. This facilitates the incorporation of limited and noisy domain knowledge, thereby allowing for an analysis of multi-view data in an inherently explainable manner. We demonstrate that our model (i) outperforms state-of-the-art approaches for modeling structured sparsity in terms of the reconstruction error and the precision/recall, (ii) robustly integrates noisy domain expertise in the form of feature sets, (iii) promotes the identifiability of factors and (iv) infers interpretable and biologically meaningful axes of variation in a real-world multi-view dataset of cancer patients.