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This paper proposes a novel framework to predict traffic flows' bandwidth ahead of time. Modern network management systems share a common issue: the network situation evolves between the moment the decision is made and the moment when…
The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics (MD) simulations is heavily dependent on the knowledge of a low dimensional manifold (parameterized by a reaction coordinate or RC)…
We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that fits the data and the manifold. We have…
Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…
Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…
Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense…
Part I of this paper considered optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network…
We consider the problem of learning a manifold from a teacher's demonstration. Extending existing approaches of learning from randomly sampled data points, we consider contexts where data may be chosen by a teacher. We analyze learning from…
Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Mapping a dataflow-graph of an ML model onto a reconfigurable system is difficult, as different mappings have different throughputs and consume resource constraints differently. To solve this, a model to evaluate the throughput of mappings…
In monocular videos that capture dynamic scenes, estimating the 3D geometry of video contents has been a fundamental challenge in computer vision. Specifically, the task is significantly challenged by the object motion, where existing…
We propose a metric learning paradigm, Regression-based Elastic Metric Learning (REML), which optimizes the elastic metric for geodesic regression on the manifold of discrete curves. Geodesic regression is most accurate when the chosen…
We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
Accurate short-term streamflow and flood forecasting are critical for mitigating river flood impacts, especially given the increasing climate variability. Machine learning-based streamflow forecasting relies on large streamflow datasets…
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds…