A general Bayesian framework is introduced for mixture modelling and inference with real-valued time series. At the top level, the state space is partitioned via the choice of a discrete context tree, so that the resulting partition depends on the values of some of the most recent samples. At the bottom level, a different model is associated with each region of the partition. This defines a very rich and flexible class of mixture models, for which we provide algorithms that allow for efficient, exact Bayesian inference. In particular, we show that the maximum a posteriori probability (MAP) model (including the relevant MAP context tree partition) can be precisely identified, along with its exact posterior probability. The utility of this general framework is illustrated in detail when a different autoregressive (AR) model is used in each state-space region, resulting in a mixture-of-AR model class. The performance of the associated algorithmic tools is demonstrated in the problems of model selection and forecasting on both simulated and real-world data, where they are found to provide results as good or better than state-of-the-art methods.

Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While many methods have been proposed to address this problem in recent years, they usually assume that the true model belongs to a known class, which is not verifiable in most real-world applications. Consequently, network modeling based on these methods either suffers from model misspecification or relies on additional model selection procedures that are not well understood in theory and can potentially be unstable in practice. To address this difficulty, we propose a mixing strategy that leverages available arbitrary models to improve their individual performances. The proposed method is computationally efficient and almost tuning-free; thus, it can be used as an off-the-shelf method for network modeling. We show that the proposed method performs equally well as the oracle estimate when the true model is included as individual candidates. More importantly, the method remains robust and outperforms all current estimates even when the models are misspecified. Extensive simulation examples are used to verify the advantage of the proposed mixing method. Evaluation of link prediction performance on 385 real-world networks from six domains also demonstrates the universal competitiveness of the mixing method across multiple domains.

Refining low-resolution (LR) spatial fields with high-resolution (HR) information is challenging as the diversity of spatial datasets often prevents direct matching of observations. Yet, when LR samples are modeled as aggregate conditional means of HR samples with respect to a mediating variable that is globally observed, the recovery of the underlying fine-grained field can be framed as taking an "inverse" of the conditional expectation, namely a deconditioning problem. In this work, we introduce conditional mean processes (CMP), a new class of Gaussian Processes describing conditional means. By treating CMPs as inter-domain features of the underlying field, a posterior for the latent field can be established as a solution to the deconditioning problem. Furthermore, we show that this solution can be viewed as a two-staged vector-valued kernel ridge regressor and show that it has a minimax optimal convergence rate under mild assumptions. Lastly, we demonstrate its proficiency in a synthetic and a real-world atmospheric field downscaling problem, showing substantial improvements over existing methods.

In this paper, we present a novel approach to identify linked fraudulent activities or actors sharing similar attributes, using Graph Convolution Network (GCN). These linked fraudulent activities can be visualized as graphs with abstract concepts like relationships and interactions, which makes GCNs an ideal solution to identify the graph edges which serve as links between fraudulent nodes. Traditional approaches like community detection require strong links between fraudulent attempts like shared attributes to find communities and the supervised solutions require large amount of training data which may not be available in fraud scenarios and work best to provide binary separation between fraudulent and non fraudulent activities. Our approach overcomes the drawbacks of traditional methods as GCNs simply learn similarities between fraudulent nodes to identify clusters of similar attempts and require much smaller dataset to learn. We demonstrate our results on linked accounts with both strong and weak links to identify fraud rings with high confidence. Our results outperform label propagation community detection and supervised GBTs algorithms in terms of solution quality and computation time.

As machine learning becomes more widely used for critical applications, the need to study its implications in privacy turns to be urgent. Given access to the target model and auxiliary information, the model inversion attack aims to infer sensitive features of the training dataset, which leads to great privacy concerns. Despite its success in grid-like domains, directly applying model inversion techniques on non-grid domains such as graph achieves poor attack performance due to the difficulty to fully exploit the intrinsic properties of graphs and attributes of nodes used in Graph Neural Networks (GNN). To bridge this gap, we present \textbf{Graph} \textbf{M}odel \textbf{I}nversion attack (GraphMI), which aims to extract private graph data of the training graph by inverting GNN, one of the state-of-the-art graph analysis tools. Specifically, we firstly propose a projected gradient module to tackle the discreteness of graph edges while preserving the sparsity and smoothness of graph features. Then we design a graph auto-encoder module to efficiently exploit graph topology, node attributes, and target model parameters for edge inference. With the proposed methods, we study the connection between model inversion risk and edge influence and show that edges with greater influence are more likely to be recovered. Extensive experiments over several public datasets demonstrate the effectiveness of our method. We also show that differential privacy in its canonical form can hardly defend our attack while preserving decent utility.

Attentional mechanisms are order-invariant. Positional encoding is a crucial component to allow attention-based deep model architectures such as Transformer to address sequences or images where the position of information matters. In this paper, we propose a novel positional encoding method based on learnable Fourier features. Instead of hard-coding each position as a token or a vector, we represent each position, which can be multi-dimensional, as a trainable encoding based on learnable Fourier feature mapping, modulated with a multi-layer perceptron. The representation is particularly advantageous for a spatial multi-dimensional position, e.g., pixel positions on an image, where $L_2$ distances or more complex positional relationships need to be captured. Our experiments based on several public benchmark tasks show that our learnable Fourier feature representation for multi-dimensional positional encoding outperforms existing methods by both improving the accuracy and allowing faster convergence.

Exploring meaningful structural regularities embedded in networks is a key to understanding and analyzing the structure and function of a network. The node-attribute information can help improve such understanding and analysis. However, most of the existing methods focus on detecting traditional communities, i.e., groupings of nodes with dense internal connections and sparse external ones. In this paper, based on the connectivity behavior of nodes and homogeneity of attributes, we propose a principle model (named GNAN), which can generate both topology information and attribute information. The new model can detect not only community structure, but also a range of other types of structure in networks, such as bipartite structure, core-periphery structure, and their mixture structure, which are collectively referred to as generalized structure. The proposed model that combines topological information and node-attribute information can detect communities more accurately than the model that only uses topology information. The dependency between attributes and communities can be automatically learned by our model and thus we can ignore the attributes that do not contain useful information. The model parameters are inferred by using the expectation-maximization algorithm. And a case study is provided to show the ability of our model in the semantic interpretability of communities. Experiments on both synthetic and real-world networks show that the new model is competitive with other state-of-the-art models.

Have you ever been in a situation where you were handing money to the clerks at a supermarket only to find that the money is fake while there was a long line of people behind you waiting to check out? I personally had experienced this situation one time and that embarrassment of being assumed to be an immoral cheapskate just stuck in my head for a long time. This motivated me to conduct this project, building a K-Means Clustering model to detect if a banknote is real or fake. This dataset is about distinguishing genuine and forged banknotes. Data were extracted from images that were taken from genuine and forged banknote-like specimens.

So what machine learning model are we building today? In this article, we are going to be building a regression model using the random forest algorithm on the solubility dataset. After model building, we are going to apply the model to make predictions followed by model performance evaluation and data visualization of its results. So which dataset are we going to use? The default answer may be to use a toy dataset as an example such as the Iris dataset (classification) or the Boston housing dataset (regression).

The representation of functions by artificial neural networks depends on a large number of parameters in a non-linear fashion. Suitable parameters of these are found by minimizing a 'loss functional', typically by stochastic gradient descent (SGD) or an advanced SGD-based algorithm. In a continuous time model for SGD with noise that follows the 'machine learning scaling', we show that in a certain noise regime, the optimization algorithm prefers 'flat' minima of the objective function in a sense which is different from the flat minimum selection of continuous time SGD with homogeneous noise.