Related papers: Estimating a Directed Tree for Extremes
We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem which is then further mapped to a modified directed polymer…
Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning…
Neural networks have proved to be very robust at processing unstructured data like images, text, videos, and audio. However, it has been observed that their performance is not up to the mark in tabular data; hence tree-based models are…
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian…
Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
Recent years have seen a notable increase in the frequency and intensity of extreme weather events. With a rising number of power outages caused by these events, accurate prediction of power line outages is essential for safe and reliable…
Bayesian networks are probabilistic graphical models often used in big data analytics. The problem of exact structure learning is to find a network structure that is optimal under certain scoring criteria. The problem is known to be NP-hard…
Neural networks with binary weights are computation-efficient and hardware-friendly, but their training is challenging because it involves a discrete optimization problem. Surprisingly, ignoring the discrete nature of the problem and using…
While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…
We propose an approach for learning optimal tree-based prescription policies directly from data, combining methods for counterfactual estimation from the causal inference literature with recent advances in training globally-optimal decision…
We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying…
Extreme weather frequently cause widespread outages in distribution systems (DSs), demonstrating the importance of hardening strategies for resilience enhancement. However, the well-utilization of real-world outage data with associated…
Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…