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Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited to deep neural networks. This balance of phenomenological…
In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…
Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble…
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…
This paper proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the…
In our previous work, we introduced the random $k$-cut number for rooted graphs. In this paper, we show that the distribution of the $k$-cut number in complete binary trees of size $n$, after rescaling, is asymptotically a periodic function…
Semantic segmentation is a crucial image understanding task, where each pixel of image is categorized into a corresponding label. Since the pixel-wise labeling for ground-truth is tedious and labor intensive, in practical applications, many…
Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target…
Recurrent stochastic configuration networks (RSCNs) have shown great potential in modelling nonlinear dynamic systems with uncertainties. This paper presents an RSCN with hybrid regularization to enhance both the learning capacity and…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, they are often treated as black-box models and as such it is difficult to understand what exactly they learn as well as…
We present Neural Random Forest Imitation - a novel approach for transforming random forests into neural networks. Existing methods propose a direct mapping and produce very inefficient architectures. In this work, we introduce an imitation…
Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and…
Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure between main effects…
Random forests construct each tree with a different, randomised representation of the feature space. Their uniform voting cannot correct errors in regions where trees with incorrect representations probabilistically outnumber correct ones,…
A fundamental task in causal inference is estimating the effect of distribution shift in the treatment variable. We refer to this problem as shift-response function (SRF) estimation. Existing neural network methods for causal inference lack…
An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability $p$…
This paper addresses the problem of approximate MAP-MRF inference in general graphical models. Following [36], we consider a family of linear programming relaxations of the problem where each relaxation is specified by a set of nested pairs…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…