Artificial Intelligence is rapidly becoming the present and future of technology. Machine learning algorithms have been created to handle challenging real-world situations. These algorithms are highly efficient and self-modifying, as they improve over time with the addition of more data and minimal human involvement. Let's go over the top machine learning algorithms you should be familiar with to keep up with the latest ML advancements. The algorithm depicts the relationship between two variables, one independent and the other dependent. When the independent variable is changed, it affects the dependent variable.

We present an end-to-end differentiable neural network architecture to perform anomaly detection in multivariate time series by incorporating a Sequential Probability Ratio Test on the prediction residual. The architecture is a cascade of dynamical systems designed to separate linearly predictable components of the signal such as trends and seasonality, from the non-linear ones. The former are modeled by local Linear Dynamic Layers, and their residual is fed to a generic Temporal Convolutional Network that also aggregates global statistics from different time series as context for the local predictions of each one. The last layer implements the anomaly detector, which exploits the temporal structure of the prediction residuals to detect both isolated point anomalies and set-point changes. It is based on a novel application of the classic CUMSUM algorithm, adapted through the use of a variational approximation of f-divergences. The model automatically adapts to the time scales of the observed signals. It approximates a SARIMA model at the get-go, and auto-tunes to the statistics of the signal and its covariates, without the need for supervision, as more data is observed. The resulting system, which we call STRIC, outperforms both state-of-the-art robust statistical methods and deep neural network architectures on multiple anomaly detection benchmarks.

Naive Bayes(NB) is one of the essential algorithms in data mining. However, it is rarely used in reality because of the attribute independent assumption. Researchers have proposed many improved NB methods to alleviate this assumption. Among these methods, due to high efficiency and easy implementation, the filter attribute weighted NB methods receive great attentions. However, there still exists several challenges, such as the poor representation ability for single index and the fusion problem of two indexes. To overcome above challenges, we propose a general framework for Adaptive Two-index Fusion attribute weighted NB(ATFNB). Two types of data description category are used to represent the correlation between classes and attributes, intercorrelation between attributes and attributes, respectively. ATFNB can select any one index from each category. Then, we introduce a switching factor \{beta} to fuse two indexes, which can adaptively adjust the optimal ratio of the two index on various datasets. And a quick algorithm is proposed to infer the optimal interval of switching factor \{beta}. Finally, the weight of each attribute is calculated using the optimal value \{beta} and is integrated into NB classifier to improve the accuracy. The experimental results on 50 benchmark datasets and a Flavia dataset show that ATFNB outperforms the basic NB and state-of-the-art filter weighted NB models. In addition, the ATFNB framework can improve the existing two-index NB model by introducing the adaptive switching factor \{beta}. Auxiliary experimental results demonstrate the improved model significantly increases the accuracy compared to the original model without the adaptive switching factor \{beta}.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Planet induced sub-structures, like annular gaps, observed in dust emission from protoplanetary disks provide a unique probe to characterize unseen young planets. While deep learning based model has an edge in characterizing the planet's properties over traditional methods, like customized simulations and empirical relations, it lacks in its ability to quantify the uncertainty associated with its predictions. In this paper, we introduce a Bayesian deep learning network "DPNNet-Bayesian" that can predict planet mass from disk gaps and provides uncertainties associated with the prediction. A unique feature of our approach is that it can distinguish between the uncertainty associated with the deep learning architecture and uncertainty inherent in the input data due to measurement noise. The model is trained on a data set generated from disk-planet simulations using the \textsc{fargo3d} hydrodynamics code with a newly implemented fixed grain size module and improved initial conditions. The Bayesian framework enables estimating a gauge/confidence interval over the validity of the prediction when applied to unknown observations. As a proof-of-concept, we apply DPNNet-Bayesian to dust gaps observed in HL Tau. The network predicts masses of $ 86.0 \pm 5.5 M_{\Earth} $, $ 43.8 \pm 3.3 M_{\Earth} $, and $ 92.2 \pm 5.1 M_{\Earth} $ respectively, which are comparable to other studies based on specialized simulations.

Fairness of machine learning algorithms has been of increasing interest. In order to suppress or eliminate discrimination in prediction, various notions as well as approaches have been proposed to impose fairness. Given a notion of fairness, an essential problem is then whether or not it can always be attained, even if with an unlimited amount of data. This issue is, however, not well addressed yet. In this paper, focusing on the Equalized Odds notion of fairness, we consider the attainability of this criterion and, furthermore, if it is attainable, the optimality of the prediction performance under various settings. In particular, for prediction performed by a deterministic function of input features, we give conditions under which Equalized Odds can hold true; if the stochastic prediction is acceptable, we show that under mild assumptions, fair predictors can always be derived. For classification, we further prove that compared to enforcing fairness by post-processing, one can always benefit from exploiting all available features during training and get potentially better prediction performance while remaining fair. Moreover, while stochastic prediction can attain Equalized Odds with theoretical guarantees, we also discuss its limitation and potential negative social impacts.

Influence diagrams have recently been used to analyse the safety and fairness properties of AI systems. A key building block for this analysis is a graphical criterion for value of information (VoI). This paper establishes the first complete graphical criterion for VoI in influence diagrams with multiple decisions. Along the way, we establish two important techniques for proving properties of multi-decision influence diagrams: ID homomorphisms are structure-preserving transformations of influence diagrams, while a Tree of Systems is collection of paths that captures how information and control can flow in an influence diagram.

A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least favorable prior distribution. The Bayesian estimator induced by a least favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits the use of popular algorithms such as projected gradient ascent to find least favorable priors. Throughout the paper, in order to make progress on the problem, we restrict ourselves to Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.

Despite its wide use and empirical successes, the theoretical understanding and study of the behaviour and performance of the variational autoencoder (VAE) have only emerged in the past few years. We contribute to this recent line of work by analysing the VAE's reconstruction ability for unseen test data, leveraging arguments from the PAC-Bayes theory. We provide generalisation bounds on the theoretical reconstruction error, and provide insights on the regularisation effect of VAE objectives. We illustrate our theoretical results with supporting experiments on classical benchmark datasets.