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Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
In this work, travel destination and business location are taken as venues. Discovering a venue by a photo is very important for context-aware applications. Unfortunately, few efforts paid attention to complicated real images such as venue…
Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling methodology for fusion and inference from multiple and massive…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
Canonical Correlation Analysis (CCA) is a method for analyzing pairs of random vectors; it learns a sequence of paired linear transformations such that the resultant canonical variates are maximally correlated within pairs while…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
In clinical and biomedical research, multiple high-dimensional datasets are nowadays routinely collected from omics and imaging devices. Multivariate methods, such as Canonical Correlation Analysis (CCA), integrate two (or more) datasets to…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Sparse Canonical Correlation Analysis (SCCA) is a fundamental statistical tool for identifying linear relationships in high-dimensional, multi-view data. While minimax theory establishes an optimal sample complexity scaling additively with…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
We present an extension of sparse Canonical Correlation Analysis (CCA) designed for finding multiple-to-multiple linear correlations within a single set of variables. Unlike CCA, which finds correlations between two sets of data where the…
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We propose MNPCA, a novel non-linear generalization of (2D)$^2${PCA}, a classical linear method for the simultaneous dimension reduction of both rows and columns of a set of matrix-valued data. MNPCA is based on optimizing over separate…
Effective medium super-cell approximation method which is introduced for disordered systems is extended to a general case of interacting disordered systems. We found that the dynamical cluster approximation (DCA) and also the non local…
Phase-amplitude coupling (PAC), a form of cross-frequency interaction, has been implicated in various cognitive functions and, by extension, in neural communication and information integration. Accurately detecting and characterising PAC is…
Whether learned, simulated, or analytical, approximations of a robot's dynamics can be inaccurate when encountering novel environments. Many approaches have been proposed to quantify the aleatoric uncertainty of such methods, i.e.…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…