Rahul Mazumder’s research while affiliated with Massachusetts Institute of Technology and other places

... Although easy to apply, these methods may result in information loss or introduce significant bias [29]. In contrast, algorithms such as k-Nearest Neighbor, Expectation-Maximization, Matrix Factorization, and Multiple Imputation using Chained Equations [20,[30][31][32] consider multiple influencing parameters of the real system and their interrelationships as comprehensively as possible, thereby reducing imputation bias. Recently, interpolation models based on Generative Adversarial Networks (GANs) [33] have achieved higher accuracy; however, their training process may encounter issues such as mode collapse and difficulty in convergence. ...

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Reconstruction and Prediction of Chaotic Time Series with Missing Data: Leveraging Dynamical Correlations Between Variables

... According to the data from Demographia (2023), there are a total of 44 megalopolises worldwide, with approximately half of them located in China and India. According to the data from the 19.87 million in its urban area, has become the first megacity in China [7,8]. However, the allocation of medical resources in the suburbs does not match the population size. ...

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Spatial–temporal analysis of patient complaints in Shanghai from 2015 to 2022

... Hajek et al. (2010) attempted to determine the statistical characterization of grain-size distributions in natural rivers. Ghoshal et al. (2013) and Ghoshal and Pal (2014) did experiments on a sand-gravel mixture to understand the bed material character in the river form, sorting process and its role in controlling the sediment flux through the landscape. Pal and Ghoshal (2014a, 2014b, 2015 in a series of papers carried out experiments on sand-gravel mixture beds under different flow velocities to study the influence of bed roughness, flow velocity, and suspension height on the grain-size distribution in suspension. ...

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Grain sorting and migration patterns of a channel bar: a dual perspective from natural and experimental studies

... In turbulent boundary layers, coherent structures with large flux events have been proposed to explain the "bursting" phenomena responsible for two types of eddy motions name as "ejections" and "sweeps" (Cantwell, 1981;Robinson, 1991). These events are traditionally detected by conditional sampling through quadrant analysis in the (x, z)-plane (Willmarth & Lu, 1972) and their statistics have been investigated for a variety of flows and wall-roughness conditions, for example, experiments in open-channel (Hurther & Lemmin, 2000;Hurther, Lemmin, & Terray, 2007;Mazumder, 2007;Mazumder, Pal, Ghoshal, & Ojha, 2009;Nakagawa & Nezu, 1977;Nelson, Shreve, McLean, & Drake, 1995;Ojha & Mazumder, 2008;Venditti & Bauer, 2005); in wind-tunnel (Raupach, 1981); under an-ice boundary layer (Fer, McPhee, & Sirevaag, 2004); in atmospheric boundary layers (Hurther & Lemmin, 2003;Katul, Kuhn, Schieldge, & Hsieh, 1997;Katul, Poggi, Cava, & Finnigan, 2006;Sterk, Jacobs, & van Boxel, 1998), and in scour around vertical circular cylinders (Debnath, Manik, & Mazumder, 2012;Kirkil, Constantinscu, & Ettema, 2008;Sarkar, Chakraborty, & Mazumder, 2015;Sarkar, Chakraborty, & Mazumder, 2016). Besides the dominant role of the sweeps close to a rough wall, an "equilibrium region" is often observed in fully developed turbulent flows (Krogstad, Antonia, & Browne, 1992). ...

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Prediction of plane-wise turbulent events to the Reynolds stress in a flow over scour-bed

... (Lyn [4], Bennett and Best [5], Parsons et al. [6], Best [7], Poggi et al. [8], Ojha and Mazumder [9], Peet et al. [10], Stoesser et al. [11], Mazumder et al. [12], Keshavarzi et al. [13]). The turbulent flow and related bursting phenomena over an isolated asymmetric waveform structure were studied statistically by Mazumder and Mazumder [14] using the analysis of multivariate normal distribution. Mazumder [15,16] studied the turbulence of fluid flow in the trough region between a pair of adjacent asymmetric waveform structures using a statistical clustering technique based on geometry and interactions of turbulence bursting rate. ...

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Turbulent flow over the trough region formed by a pair of forward-facing bedform shapes

... In terms of DC structure in sparse regularization, several works have analyzed the use of the DC function x → ∥x∥ 1 − ∥x∥ 2 as a sparsity inducing regularizer [3,51] as its zeros correspond to 1-sparse vectors. Many popular nonconvex regularizers have also been shown to have a DC decomposition [12], such as SCAD [18], MCP [53], or the Logarithmic penalty [35]. ...

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Learning Difference-of-Convex Regularizers for Inverse Problems: A Flexible Framework with Theoretical Guarantees

... Thus, the spectrum of a balanced signed graph G b is equivalent to the spectrum of the corresponding positive graph G + , and developed spectral filters for positive graphs can be reused for balanced signed graphs. However, existing GL methods computing balanced signed graphs are limited to sub-optimal two-step approaches 1 : first compute a signed graph from data using, for example, graphical lasso (GLASSO) [23], then balance the computed graph via ad-hoc and often computation-expensive balancing algorithms [24]- [27]. ...

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Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

... Hence, using this information as user covariates helps in improving predictions for explicit ratings. Further, one can derive an item graph where edge weights represent movie similarities that are based on global "who-rated-what" matrix (Kouki et al., 2015;Wang et al., 2015;Agarwal et al., 2011;Mazumder and Agarwal, 2011). Imposing sparsity on such a graph and finding its fair communities is attractive since it is intuitive that an item is generally related to only a few other items. ...

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Fair Structure Learning in Heterogeneous Graphical Models

... We follow the experimental setting in [15,12,11] to generate data and perform synthetic experiments on multivariate Gaussians. Each off-diagonal entry of the precision matrix is drawn from a uniform distribution, i.e., Θ * ij ∼ U(−1, 1), and then set to zero with probability p = 1 − s, where s means the sparsity level (refer to Appendix C.1). ...

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GLAD: Learning Sparse Graph Recovery

... This is of interest because L R = O q implies that there are no across-block edges so that the two groups are independent. For the case where λ 2 = 0, i.e. in the graphical lasso, this problem was considered by Witten et al. (2011) and Mazumder and Hastie (2012) where it is proved that such block diagonal structure is obtained whenever λ 1 ≥ max i, j∈L |s i j |. Here, we show that the latter result is still true in the pdglasso problem for any λ 2 ≥ 0. ...

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On the application of Gaussian graphical models to paired data problems