Related papers: A robust method for fitting degree distributions o…
As deep learning models and datasets rapidly scale up, network training is extremely time-consuming and resource-costly. Instead of training on the entire dataset, learning with a small synthetic dataset becomes an efficient solution.…
With the rise of big data, networks have pervaded many aspects of our daily lives, with applications ranging from the social to natural sciences. Understanding the latent structure of the network is thus an important question. In this…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…
This paper is a step-by-step tutorial for fitting a mixture distribution to data. It merely assumes the reader has the background of calculus and linear algebra. Other required background is briefly reviewed before explaining the main…
It is commonly believed that real networks are scale-free and fraction of nodes $P(k)$ with degree $k$ satisfies the power law $P(k) \propto k^{-\gamma} \text{ for } k > k_{min} > 0$. Preferential attachment is the mechanism that has been…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
In scientific machine learning, models are routinely deployed with parameter values or boundary conditions far from those used in training. This paper studies the learning-where-to-learn problem of designing a training data distribution…
We study the task of selecting $k$ nodes, in a social network of size $n$, to seed a diffusion with maximum expected spread size, under the independent cascade model with cascade probability $p$. Most of the previous work on this problem…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…
In a multifidelity setting, data are available under the same conditions from two (or more) sources, e.g. computer codes, one being lower-fidelity but computationally cheaper, and the other higher-fidelity and more expensive. This work…
Theoretical frameworks to estimate the tolerance of metabolic networks to various failures are important to evaluate the robustness of biological complex systems in systems biology. In this paper, we focus on a measure for robustness in…
Preferential attachment models have been widely studied in complex networks, because they can explain the formation of many networks like social networks, citation networks, power grids, and biological networks, to name a few. Motivated by…
In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…
This paper presents adaptive link selection algorithms for distributed estimation and considers their application to wireless sensor networks and smart grids. In particular, exhaustive search--based least--mean--squares(LMS)/recursive least…
Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
In this paper, we adopt a probability distribution estimation perspective to explore the optimization mechanisms of supervised classification using deep neural networks. We demonstrate that, when employing the Fenchel-Young loss, despite…