Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.

While many approaches exist in the literature to learn representations for data collections in multiple modalities, the generalizability of the learnt representations to previously unseen data is a largely overlooked subject. In this work, we first present a theoretical analysis of learning multi-modal nonlinear embeddings in a supervised setting. Our performance bounds indicate that for successful generalization in multi-modal classification and retrieval problems, the regularity of the interpolation functions extending the embedding to the whole data space is as important as the between-class separation and cross-modal alignment criteria. We then propose a multi-modal nonlinear representation learning algorithm that is motivated by these theoretical findings, where the embeddings of the training samples are optimized jointly with the Lipschitz regularity of the interpolators. Experimental comparison to recent multi-modal and single-modal learning algorithms suggests that the proposed method yields promising performance in multi-modal image classification and cross-modal image-text retrieval applications.

Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus on maximizing the margin has been well motivated through numerous generalization bounds. In this paper, we revisit and improve the classic generalization bounds in terms of margins. Furthermore, we complement our new generalization bound by a nearly matching lower bound, thus almost settling the generalization performance of SVMs in terms of margins.

The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families of functions: (i) convex functions supported on a polytope (in fixed design), (ii) bounded convex functions supported on a polytope (in random design), and (iii) convex Lipschitz functions supported on any convex domain (in random design). For each of these families, the risk of the LSE is proved to be of the order $n^{-2/d}$ (up to logarithmic factors) while the minimax risk is $n^{-4/(d+4)}$, for $d \ge 5$. In addition, the first rate of convergence results (worst case and adaptive) for the full convex LSE are established for polytopal domains for all $d \geq 1$. Some new metric entropy results for convex functions are also proved which are of independent interest.

Hierarchical forecasting methods have been widely used to support aligned decision-making by providing coherent forecasts at different aggregation levels. Traditional hierarchical forecasting approaches, such as the bottom-up and top-down methods, focus on a particular aggregation level to anchor the forecasts. During the past decades, these have been replaced by a variety of linear combination approaches that exploit information from the complete hierarchy to produce more accurate forecasts. However, the performance of these combination methods depends on the particularities of the examined series and their relationships. This paper proposes a novel hierarchical forecasting approach based on machine learning that deals with these limitations in three important ways. First, the proposed method allows for a non-linear combination of the base forecasts, thus being more general than the linear approaches. Second, it structurally combines the objectives of improved post-sample empirical forecasting accuracy and coherence. Finally, due to its non-linear nature, our approach selectively combines the base forecasts in a direct and automated way without requiring that the complete information must be used for producing reconciled forecasts for each series and level. The proposed method is evaluated both in terms of accuracy and bias using two different data sets coming from the tourism and retail industries. Our results suggest that the proposed method gives superior point forecasts than existing approaches, especially when the series comprising the hierarchy are not characterized by the same patterns.

Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate posterior density, combining it with Monte Carlo sampling methods and other quadrature rules. The nodes of the quadrature are sequentially chosen by maximizing a suitable acquisition function, which takes into account the current approximation of the posterior and the positions of the nodes. This maximization does not require additional evaluations of the true posterior. We introduce two specific schemes based on Gaussian and Nearest Neighbors (NN) bases. For the Gaussian case, we also provide a novel procedure for fitting the bandwidth parameter, in order to build a suitable emulator of a density function. With both techniques, we always obtain a positive estimation of the marginal likelihood (a.k.a., Bayesian evidence). An equivalent importance sampling interpretation is also described, which allows the design of extended schemes. Several theoretical results are provided and discussed. Numerical results show the advantage of the proposed approach, including a challenging inference problem in an astronomic dynamical model, with the goal of revealing the number of planets orbiting a star.

Machine learning, the subset of artificial intelligence that teaches computers to perform tasks through examples and experience, is a hot area of research and development. Many of the applications we use daily use machine learning algorithms, including AI assistants, web search and machine translation. Your social media news feed is powered by a machine learning algorithm. The recommended videos you see on YouTube and Netflix are the result of a machine learning model. And Spotify's Discover Weekly draws on the power of machine learning algorithms to create a list of songs that conform to your preferences. But machine learning comes in many different flavors.

We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems, including history matching. The developed technique is based on principal component analysis (PCA) but modifies a purely data-driven basis of principal components considering objective function behavior. To define an efficient encoding, Gradient-Sensitive PCA uses an objective function gradient with respect to model parameters. We propose computationally efficient implementations of the technique, and two of them are based on stationary perturbation theory (SPT). Optimality, correctness, and low computational costs of the new encoding approach are tested, verified, and discussed. Three algorithms for optimal parameter decomposition are presented and applied to an objective of 2D synthetic history matching. The results demonstrate improvements in encoding quality regarding objective function minimization and distributional patterns of the desired field. Possible applications and extensions are proposed.

To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of quantum mechanics, canonically conjugate observables such as position and momentum cannot both be distinctly determined in any quantum state. In the same manner, the branch of Spectral filtering design implies that a nonzero function and its Fourier transform cannot both be sharply localized. After delving into such concepts on Uncertainty Principle and their variations in quantum physics, Fourier analysis, and wavelet design, the proposed framework is described in terms of algorithm and flowchart. Our proposed optimizer's idea is based on an inherent uncertainty in performing local search versus global solution search. A set of compatible metrics for each part of the framework is proposed to derive preferred form of algorithm. Evaluations and comparisons at the end of paper show competency and distinct capability of the algorithm over some of the well-known and recently proposed metaheuristics.

Knowledge Graphs (KGs) have gained considerable attention recently from both academia and industry. In fact, incorporating graph technology and the copious of various graph datasets have led the research community to build sophisticated graph analytics tools. Therefore, the application of KGs has extended to tackle a plethora of real-life problems in dissimilar domains. Despite the abundance of the currently proliferated generic KGs, there is a vital need to construct domain-specific KGs. Further, quality and credibility should be assimilated in the process of constructing and augmenting KGs, particularly those propagated from mixed-quality resources such as social media data. This paper presents a novel credibility domain-based KG Embedding framework. This framework involves capturing a fusion of data obtained from heterogeneous resources into a formal KG representation depicted by a domain ontology. The proposed approach makes use of various knowledge-based repositories to enrich the semantics of the textual contents, thereby facilitating the interoperability of information. The proposed framework also embodies a credibility module to ensure data quality and trustworthiness. The constructed KG is then embedded in a low-dimension semantically-continuous space using several embedding techniques. The utility of the constructed KG and its embeddings is demonstrated and substantiated on link prediction, clustering, and visualisation tasks.