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Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…

Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…

We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…

In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing…

Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…

Deep convolutional neural networks (DCNN) have enjoyed great successes in many signal processing applications because they can learn complex, non-linear causal relationships from input to output. In this light, DCNNs are well suited for the…

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The…

Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…

We present a loss function for neural networks that encompasses an idea of trivial versus non-trivial predictions, such that the network jointly determines its own prediction goals and learns to satisfy them. This permits the network to…

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…