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Estimation of Shortest Path Covariance Matrices [article]

Raj Kumar Maity, Cameron Musco
2020 arXiv   pre-print
We study the sample complexity of estimating the covariance matrix Σ∈ℝ^d× d of a distribution 𝒟 over ℝ^d given independent samples, under the assumption that Σ is graph-structured. In particular, we focus on shortest path covariance matrices, where the covariance between any two measurements is determined by the shortest path distance in an underlying graph with d nodes. Such matrices generalize Toeplitz and circulant covariance matrices and are widely applied in signal processing applications,
more » ... where the covariance between two measurements depends on the (shortest path) distance between them in time or space. We focus on minimizing both the vector sample complexity: the number of samples drawn from 𝒟 and the entry sample complexity: the number of entries read in each sample. The entry sample complexity corresponds to measurement equipment costs in signal processing applications. We give a very simple algorithm for estimating Σ up to spectral norm error ϵΣ_2 using just O(√(D)) entry sample complexity and Õ(r^2/ϵ^2) vector sample complexity, where D is the diameter of the underlying graph and r ≤ d is the rank of Σ. Our method is based on extending the widely applied idea of sparse rulers for Toeplitz covariance estimation to the graph setting. In the special case when Σ is a low-rank Toeplitz matrix, our result matches the state-of-the-art, with a far simpler proof. We also give an information theoretic lower bound matching our upper bound up to a factor D and discuss some directions towards closing this gap.
arXiv:2011.09986v1 fatcat:2mortzq7hraerhe36jkgdkfade

Shaping Proto-Value Functions via Rewards [article]

Chandrashekar Lakshmi Narayanan, Raj Kumar Maity, Shalabh Bhatnagar
2015 arXiv   pre-print
In this paper, we combine task-dependent reward shaping and task-independent proto-value functions to obtain reward dependent proto-value functions (RPVFs). In constructing the RPVFs we are making use of the immediate rewards which are available during the sampling phase but are not used in the PVF construction. We show via experiments that learning with an RPVF based representation is better than learning with just reward shaping or PVFs. In particular, when the state space is symmetrical and
more » ... he rewards are asymmetrical, the RPVF capture the asymmetry better than the PVFs.
arXiv:1511.08589v1 fatcat:h7bhv3romraqpeyxlnkwb5ld2e

Distributed Newton Can Communicate Less and Resist Byzantine Workers [article]

Avishek Ghosh, Raj Kumar Maity, Arya Mazumdar
2020 arXiv   pre-print
We develop a distributed second order optimization algorithm that is communication-efficient as well as robust against Byzantine failures of the worker machines. We propose COMRADE (COMunication-efficient and Robust Approximate Distributed nEwton), an iterative second order algorithm, where the worker machines communicate only once per iteration with the center machine. This is in sharp contrast with the state-of-the-art distributed second order algorithms like GIANT [34] and DINGO[7], where
more » ... worker machines send (functions of) local gradient and Hessian sequentially; thus ending up communicating twice with the center machine per iteration. Moreover, we show that the worker machines can further compress the local information before sending it to the center. In addition, we employ a simple norm based thresholding rule to filter-out the Byzantine worker machines. We establish the linear-quadratic rate of convergence of COMRADE and establish that the communication savings and Byzantine resilience result in only a small statistical error rate for arbitrary convex loss functions. To the best of our knowledge, this is the first work that addresses the issue of Byzantine resilience in second order distributed optimization. Furthermore, we validate our theoretical results with extensive experiments on synthetic and benchmark LIBSVM [5] data-sets and demonstrate convergence guarantees.
arXiv:2006.08737v1 fatcat:b4nsluk4dfblpjcowcnkhuuyom

Robust Gradient Descent via Moment Encoding with LDPC Codes [article]

Raj Kumar Maity, Ankit Singh Rawat, Arya Mazumdar
2019 arXiv   pre-print
This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of straggling processors. To mitigate the effect of the stragglers, it has been previously proposed to encode the data with an erasure-correcting code and decode at the master server at the end of the computation. We, instead, propose to encode the second-moment of the data with a low density parity-check (LDPC) code. The iterative decoding algorithms for
more » ... PC codes have very low computational overhead and the number of decoding iterations can be made to automatically adjust with the number of stragglers in the system. We show that for a random model for stragglers, the proposed moment encoding based gradient descent method can be viewed as the stochastic gradient descent method. This allows us to obtain convergence guarantees for the proposed solution. Furthermore, the proposed moment encoding based method is shown to outperform the existing schemes in a real distributed computing setup.
arXiv:1805.08327v2 fatcat:bghtp26hhjbutjnxx6jffb3e5q

High Dimensional Discrete Integration over the Hypergrid [article]

Raj Kumar Maity, Arya Mazumdar, Soumyabrata Pal
2019 arXiv   pre-print
Recently Ermon et al. (2013) pioneered a way to practically compute approximations to large scale counting or discrete integration problems by using random hashes. The hashes are used to reduce the counting problem into many separate discrete optimization problems. The optimization problems then can be solved by an NP-oracle such as commercial SAT solvers or integer linear programming (ILP) solvers. In particular, Ermon et al. showed that if the domain of integration is {0,1}^n then it is
more » ... le to obtain a solution within a factor of 16 of the optimal (a 16-approximation) by this technique. In many crucial counting tasks, such as computation of partition function of ferromagnetic Potts model, the domain of integration is naturally {0,1,..., q-1}^n, q>2, the hypergrid. The straightforward extension of Ermon et al.'s method allows a q^2-approximation for this problem. For large values of q, this is undesirable. In this paper, we show an improved technique to obtain an approximation factor of 4+O(1/q^2) to this problem. We are able to achieve this by using an idea of optimization over multiple bins of the hash functions, that can be easily implemented by inequality constraints, or even in unconstrained way. Also the burden on the NP-oracle is not increased by our method (an ILP solver can still be used). We provide experimental simulation results to support the theoretical guarantees of our algorithms.
arXiv:1806.11542v3 fatcat:5dwcqluq3jfwhjt4ywbqhxbxsm

A workload-adaptive mechanism for linear queries under local differential privacy [article]

Ryan McKenna, Raj Kumar Maity, Arya Mazumdar, Gerome Miklau
2020 arXiv   pre-print
We propose a new mechanism to accurately answer a user-provided set of linear counting queries under local differential privacy (LDP). Given a set of linear counting queries (the workload) our mechanism automatically adapts to provide accuracy on the workload queries. We define a parametric class of mechanisms that produce unbiased estimates of the workload, and formulate a constrained optimization problem to select a mechanism from this class that minimizes expected total squared error. We
more » ... e this optimization problem numerically using projected gradient descent and provide an efficient implementation that scales to large workloads. We demonstrate the effectiveness of our optimization-based approach in a wide variety of settings, showing that it outperforms many competitors, even outperforming existing mechanisms on the workloads for which they were intended.
arXiv:2002.01582v2 fatcat:rwfyl437hbdsjnqrznmf5o6o2i

Poly(lactic-co-glycolic acid)-loaded nanoparticles of betulinic acid for improved treatment of hepatic cancer: characterization, in vitro and in vivo evaluations

Pranesh Kumar, Ashok K Singh, Vinit Raj, Amit Rai, Amit K Keshari, Dinesh Kumar, Biswanath Maity, Anand Prakash, Sabyasachi Maiti, Sudipta Saha
2018 International Journal of Nanomedicine  
The application of betulinic acid (B), a potent antineoplastic agent, is limited due to poor bioavailability, short plasma half-life and inappropriate tissue distribution. Thus, we aimed to prepare novel 50:50 poly(lactic-co-glycolic acid) (PLGA)-loaded B nanoparticles (BNP) and to compare its anti-hepatocellular carcinoma (HCC) activity with parent B. BNP were synthesized and characterized using different methods such as scanning electron microscopy (SEM), fourier-transform infrared (FTIR)
more » ... trometry and particle size analyses. Particle size of BNP was optimized through the application of the stabilizer, polyvinyl alcohol (PVA). The anti-HCC response was evaluated through in vitro cell line study using Hep-G2 cells, confocal microscopy, in vivo oral pharmacokinetics and animal studies. Further, quantitative reverse transcription polymerase chain reaction (qRT-PCR) analysis was conducted to observe the changes in the expression of specific genes. Particle size of BNP was optimized through the application of the stabilizer, polyvinyl alcohol. Physicochemical characterization exhibited particle size of 257.1 nm with zeta potential -0.170 mV (optimized batch B, BNP). SEM and FTIR analyses of BNP showed that cylindrical particles of B converted to spherical particles in BNP and there were no interaction between B and used polymers. The release study of optimized BNP was highest (≥80%) than any other formulation. Later, in vitro cell culture analysis using Hep-G2 cells and confocal microscopy studies revealed that BNP had the highest inhibition and penetration properties than parent B. Oral pharmacokinetics studies using albino Wistar rats at single 100 mg dose again exhibited BNP had the higher 50% of plasma concentration (t1/2), a higher maximum plasma concentration (Cmax) and took longer to reach the maximum plasma concentration (Tmax) than parent B. Next, our in vivo study using nitrosodiethyl amine (NDEA)-induced HCC model documented BNP decreased in number of nodules, restored body weight, oxidative stress parameters, liver marker enzymes and histological architecture than parent B. Lastly, qRT-PCR studies further demonstrated that anti-HCC properties of BNP may be due to over expression of antiapoptotic caspases i.e., caspase 3 and 8. The prepared BNP showed a better therapeutic response against HCC and could be attributed as future candidate molecule for HCC treatment.
doi:10.2147/ijn.s157391 pmid:29497292 pmcid:PMC5818879 fatcat:jvo2srfzgnf37ls5o2qv2lvec4

vqSGD: Vector Quantized Stochastic Gradient Descent [article]

Venkata Gandikota, Daniel Kane, Raj Kumar Maity, Arya Mazumdar
2020 arXiv   pre-print
In this work, we present a family of vector quantization schemes vqSGD (Vector-Quantized Stochastic Gradient Descent) that provide an asymptotic reduction in the communication cost with convergence guarantees in first-order distributed optimization. In the process we derive the following fundamental information theoretic fact: Θ(d/R^2) bits are necessary and sufficient to describe an unbiased estimator ĝ(g) for any g in the d-dimensional unit sphere, under the constraint that ĝ(g)_2≤ R almost
more » ... rely. In particular, we consider a randomized scheme based on the convex hull of a point set, that returns an unbiased estimator of a d-dimensional gradient vector with almost surely bounded norm. We provide multiple efficient instances of our scheme, that are near optimal, and require only o(d) bits of communication at the expense of tolerable increase in error. The instances of our quantization scheme are obtained using the properties of binary error-correcting codes and provide a smooth tradeoff between the communication and the estimation error of quantization. Furthermore, we show that vqSGD also offers strong privacy guarantees.
arXiv:1911.07971v4 fatcat:ddu2enkm2bf4tffbqffdmhv7ra

6,7-dimethoxy-1,2,3,4-tetrahydro-isoquinoline-3-carboxylic acid attenuates heptatocellular carcinoma in rats with NMR-based metabolic perturbations

Pranesh Kumar, Ashok K Singh, Vinit Raj, Amit Rai, Siddhartha Maity, Atul Rawat, Umesh Kumar, Dinesh Kumar, Anand Prakash, Anupam Guleria, Sudipta Saha
2017 Future Science OA  
Quality control (QC) samples were also future science group future science group Research Article Kumar, Singh, Raj et al.  ...  P Kumar, V Raj, A Rai and S Saha performed pharmacological screening. AK Singh and S Saha performed synthesis of M1, docking and statistical data analysis.  ... 
doi:10.4155/fsoa-2017-0008 pmid:28884001 pmcid:PMC5583658 fatcat:vi2sxmmhbfbu3dsrw4zfl4rpfa

Novel Indole-fused benzo-oxazepines (IFBOs) inhibit invasion of hepatocellular carcinoma by targeting IL-6 mediated JAK2/STAT3 oncogenic signals

Ashok K. Singh, Archana S. Bhadauria, Umesh Kumar, Vinit Raj, Amit Rai, Pranesh Kumar, Amit K. Keshari, Dinesh Kumar, Biswanath Maity, Sneha Nath, Anand Prakash, Sudipta Saha
2018 Scientific Reports  
Inspired by the well-documented tumor protecting ability of paullones, recently, we synthesized novel paullone-like scaffolds, indole-fused benzo-oxazepines (IFBOs), and screened them against hepatocellular carcinoma (HCC) specific Hep-G2 cells. Three of the synthesized compounds significantly attenuated the progression of HCC in vitro. By computational studies, we further discovered that IFBOs exhibited a stable binding complex with the IL-6 receptor. In this context, we investigated in vivo
more » ... udy using the nitrosodiethyl amine (NDEA)-induced HCC model, which strengthened our previous findings by showing the blockade of the IL-6 mediated JAK2/STAT3 oncogenic signaling pathway. Treatment with IFBOs showed remarkable attenuation of cellular proliferation, as evidenced through a decrease in the number of nodules, restoration of body weight, oxidative stress parameters, liver marker enzymes and histological architecture. Interestingly, using a metabolomic approach we further discovered that IFBOs can restore the perturbed metabolic profile associated with the HCC condition to normalcy. Particularly, the efficacy of compound 6a for an anti-HCC response was significantly better than the marketed chemotherapeutic drug, 5-fluorouracil. Altogether, these remarkable findings open up possibilities of developing IFBOs as novel future candidate molecules for plausible alternatives for HCC treatment. Hepatocellular carcinoma (HCC) is one of the most lethal cancers and has limited treatment options 1 . This is probably due to the fact that the precise mechanisms causing HCC pathogenicity are still unclear 2 . The response rate of sorafenib, the only FDA-approved drug for HCC therapy, is very limited despite its established efficacy 3 . Most of the sorafenib-treated patients experience disease recurrence by local metastasis and chemotherapeutic resistance 4 . Thus, the rational design of novel molecules targeting HCC specific pathways is imperative for improved therapy. The well-documented CDK1 inhibitors, "paullones, " are structurally based on indole-fused benzazepinone and can be used as biochemical tools in cancer drug discovery 5 . As evidenced through previous reports, the in vitro antitumor activities of a variety of paullones do not parallel with their CDK1 inhibitory properties. This finding suggests that CDKs are rather unlikely to be the critical targets responsible for the anticancer activity of paullones. Further, to potentiate the antitumor effect of paullone ring and to explore the precise mechanism of action, literatures provide two suggestions: (1) rational modifications in paullone ring structure to enhance cytotxicity, and (2) exploration of a specific target to identify the mechanism underlying paullone-modified
doi:10.1038/s41598-018-24288-0 pmid:29651140 pmcid:PMC5897576 fatcat:wgwzmnupnvhcljpxax7bqw7664

5H-benzo[h]thiazolo[2,3-b]quinazolines ameliorate NDEA-induced hepatocellular carcinogenesis in rats through IL-6 downregulation along with oxidative and metabolic stress reduction

Amit K Keshari, Ashok K Singh, Umesh Kumar, Vinit Raj, Amit Rai, Pranesh Kumar, Dinesh Kumar, Biswanath Maity, Sneha Nath, Anand Prakash, Sudipta Saha
2017 Drug Design, Development and Therapy  
: Amit K Keshari, Sudipto Saha, Biswanath Maity, Dinesh Kumar, Anand Prakash; wrote the manuscript: Amit K Keshari, Sudipto Saha, Biswanath Maity, Dinesh Kumar, Anand Prakash.  ...  Acknowledgments Author contributions Study protocol design: Sudipto Saha, Amit K Keshari; pharmacological screening: Amit K Keshari, Ashok K Singh, Pranesh Kumar, Vinit Raj, Amit Rai, Sudipto Saha; NMRbased  ... 
doi:10.2147/dddt.s143075 pmid:29075102 pmcid:PMC5648320 fatcat:q34waujcangptknrlfsyki6y6i

Ti doped BaMnO3 perovskite structure as photocatalytic agent for the degradation of noxious air and water pollutants

Siddharth Singh, Soumitra Maiti, Sonia Rani, Hari Raj, Ravindra Singh Bisht, Soraj Kumar Panigrahi, Inderjeet Tyagi
2020 SN Applied Sciences  
Photocatalytic degradation of noxious water and air impurities like Methylene blue (MB), Rhodamine B (RhB), NO x-, and CO is carried out by pristine and Ti-doped BaMnO 3 (BaMn 0.85 Ti 0.15 O 2.93 , BMT). Perovskite BMT ceramic mixed with equimolar ratio of zeolite is used for investigation of water and air pollutant degradation. The synthesized Ti-doped BaMnO 3 (BaMn 0.85 Ti 0.15 O 2.93 , BMT) perovskite was characterized using X-ray diffraction (XRD) and FE-SEM techniques. The XRD pattern of
more » ... -doped BaMnO 3 shows the formation of two phases, namely BaMnO 2.92 and BaMn 0.85 Ti 0.15 O 2.93 and BMT. The photocatalytic degradation of noxious water and air pollutants were analyzed using UV-Vis and XPS for doped and pristine BaMnO 3 . From obtained results, it is observed that the synthesized BMT shows enhanced photocatalytic degradation (~ 99%) as compared to BaMnO 3 toward noxious water impurities like RhB and MB dyes within 270 and 150 min under sunlight. The synthesized BMT compound shows the absorbance spectrum in the wavelength range of 200-600 nm. The UV-Vis DRS confirms the absorption edges for the compound above 400 nm i.e., visible light absorber with a bandgap 2.48 eV. On the other hand, XPS analysis of bulk BMT-zeolite on exposure to sunlight shows the complete degradation of adsorbed NO x gases from the BMT-zeolite surface as compared to the unexposed zeolite sample surface. Therefore, BMT can be used as active photocatalytic agent for the remediation of environmental noxious water and air pollutants.
doi:10.1007/s42452-020-2121-9 fatcat:5dbrqtb4yzg2nkjn2s5upnrxky

Assessment of Cisplatin, Etoposide, Vinblastine and Piper betle Leaf Extract on Some Attributes of Cell Division in Lathyrus sativus L

Aveek Samanta, Siraj Datta, Animesh Kumar Datta, Tilak Raj Maity, Aninda Mandal, Debadrito Das
2015 CYTOLOGIA  
Preparation of PbLE The PbLE extract is prepared as per Maity et al. (2014) .  ...  containing hydroxychavicol fraction is reported to be a potential source for prostate cancer management (Paranjpe et al. 2013 ) as well as a treatment of myeloid leukemia in animals and human beings (Kumar  ... 
doi:10.1508/cytologia.80.483 fatcat:kpuzu76axbgqvk7sk52sefcfdy

Effect of etoposide on grass pea DNA topoisomerase II: an in silico, in vivo, and in vitro assessments

Aveek Samanta, Tilak Raj Maity, Sudip Das, Animesh Kumar Datta, Siraj Datta
2019 Bulletin of the National Research Centre  
Etoposide is one of the most potential anti-cancerous drugs that targets topoisomerase II (topoII) and inhibits its activity by ligation with the DNA molecule. Results: In silico study confirmed that the etoposide-binding sites of topoII are conserved among the plants and human. The efficacy of the drug on plant system was initially assessed using germinated grass pea (Lathyrus sativus L.) seedlings (in vivo) in relation to radicle length and mitotic index. The callus system (in vitro) was also
more » ... used to elucidate the effect of etoposide on callus growth kinetics. Furthermore, it was observed that etoposide able to inhibit the division of polyploid cells induced by colchicine treatment (0.5%, 8 h). To determine the molecular interaction, topoII was isolated from young grass pea leaves using polyethylene glycol fractionation and ammonium sulphate precipitation followed by column chromatography on CM-Sephadex (C-25). The plasmid linearization assays by isolated plant topoII in the presence of etoposide significantly revealed the functional similarity of plants and human topoII. Results indicated that the effect of etoposide on plant topoII is significant. Conclusions: This study may pave the way to develop a plant-based assay system for screening the topoisomerase targeted anti-cancerous drugs, as it is convenient and cost-effective.
doi:10.1186/s42269-019-0217-4 fatcat:cbt3bgswpjcjphvdsfxlmkngka

Communication-Efficient and Byzantine-Robust Distributed Learning with Error Feedback [article]

Avishek Ghosh, Raj Kumar Maity, Swanand Kadhe, Arya Mazumdar, Kannan Ramchandran
2021 arXiv   pre-print
Raj Kumar Maity is with CS department, UMass Amherst Arya Mazumdar is with Halicioglu Data Science Institute, UC San Diego.  ...  Raj Kumar Maity and Arya Mazumdar are supported by NSF grants NSF CCF 1642658 and 1618512. Swanand Kadhe is supported in part by National Science Foundation grants CCF-1748585 and CNS-1748692 X.  ... 
arXiv:1911.09721v5 fatcat:dwzoa4mjfrdspn2etv63a43ecq
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