arXiv subjects

Shikha Singh

Publications and source records attributed to Shikha Singh.

23 records · Page 2Linked to original sources

arXiv2017

Rational Proofs with Multiple Provers

Interactive proofs (IP) model a world where a verifier delegates computation to an untrustworthy prover, verifying the prover's claims before accepting them. IP protocols have applications in areas such as verifiable computation outsourcing, computation delegation, cloud computing. In these applications, the verifier may pay the prover based on the quality of his work. Rational interactive proofs (RIP), introduced by Azar and Micali (2012), are an interactive-proof system with payments, in which the prover is rational rather than untrustworthy---he may lie, but only to increase his payment. Rational proofs leverage the provers' rationality to obtain simple and efficient protocols. Azar and Micali show that RIP=IP(=PSAPCE). They leave the question of whether multiple provers are more powerful than a single prover for rational and classical proofs as an open problem. In this paper, we introduce multi-prover rational interactive proofs (MRIP). Here, a verifier cross-checks the provers' answers with each other and pays them according to the messages exchanged. The provers are cooperative and maximize their total expected payment if and only if the verifier learns the correct answer to the problem. We further refine the model of MRIP to incorporate utility gap, which is the loss in payment suffered by provers who mislead the verifier to the wrong answer. We define the class of MRIP protocols with constant, noticeable and negligible utility gaps. We give tight characterization for all three MRIP classes. We show that under standard complexity-theoretic assumptions, MRIP is more powerful than both RIP and MIP ; and this is true even the utility gap is required to be constant. Furthermore the full power of each MRIP class can be achieved using only two provers and three rounds. (A preliminary version of this paper appeared at ITCS 2016. This is the full version that contains new results.)

cs.CC↗

arXiv2016

Deep Blind Compressed Sensing

This work addresses the problem of extracting deeply learned features directly from compressive measurements. There has been no work in this area. Existing deep learning tools only give good results when applied on the full signal, that too usually after preprocessing. These techniques require the signal to be reconstructed first. In this work we show that by learning directly from the compressed domain, considerably better results can be obtained. This work extends the recently proposed framework of deep matrix factorization in combination with blind compressed sensing; hence the term deep blind compressed sensing. Simulation experiments have been carried out on imaging via single pixel camera, under-sampled biomedical signals, arising in wireless body area network and compressive hyperspectral imaging. In all cases, the superiority of our proposed deep blind compressed sensing can be envisaged.

cs.CV↗

arXiv2016

How to Train Your Deep Neural Network with Dictionary Learning

Currently there are two predominant ways to train deep neural networks. The first one uses restricted Boltzmann machine (RBM) and the second one autoencoders. RBMs are stacked in layers to form deep belief network (DBN); the final representation layer is attached to the target to complete the deep neural network. Autoencoders are nested one inside the other to form stacked autoencoders; once the stcaked autoencoder is learnt the decoder portion is detached and the target attached to the deepest layer of the encoder to form the deep neural network. This work proposes a new approach to train deep neural networks using dictionary learning as the basic building block; the idea is to use the features from the shallower layer as inputs for training the next deeper layer. One can use any type of dictionary learning (unsupervised, supervised, discriminative etc.) as basic units till the pre-final layer. In the final layer one needs to use the label consistent dictionary learning formulation for classification. We compare our proposed framework with existing state-of-the-art deep learning techniques on benchmark problems; we are always within the top 10 results. In actual problems of age and gender classification, we are better than the best known techniques.

cs.LG↗

arXiv2016

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $ε>0$, removes at most $m-k$ demands and has cost no more than $O(1/ε^{2})$ times the cost of an optimal algorithm that removes at most $(1-ε)(m-k)$ demands.

cs.DS↗

arXiv2015

Run Generation Revisited: What Goes Up May or May Not Come Down

In this paper, we revisit the classic problem of run generation. Run generation is the first phase of external-memory sorting, where the objective is to scan through the data, reorder elements using a small buffer of size M , and output runs (contiguously sorted chunks of elements) that are as long as possible. We develop algorithms for minimizing the total number of runs (or equivalently, maximizing the average run length) when the runs are allowed to be sorted or reverse sorted. We study the problem in the online setting, both with and without resource augmentation, and in the offline setting. (1) We analyze alternating-up-down replacement selection (runs alternate between sorted and reverse sorted), which was studied by Knuth as far back as 1963. We show that this simple policy is asymptotically optimal. Specifically, we show that alternating-up-down replacement selection is 2-competitive and no deterministic online algorithm can perform better. (2) We give online algorithms having smaller competitive ratios with resource augmentation. Specifically, we exhibit a deterministic algorithm that, when given a buffer of size 4M , is able to match or beat any optimal algorithm having a buffer of size M . Furthermore, we present a randomized online algorithm which is 7/4-competitive when given a buffer twice that of the optimal. (3) We demonstrate that performance can also be improved with a small amount of foresight. We give an algorithm, which is 3/2-competitive, with foreknowledge of the next 3M elements of the input stream. For the extreme case where all future elements are known, we design a PTAS for computing the optimal strategy a run generation algorithm must follow. (4) Finally, we present algorithms tailored for nearly sorted inputs which are guaranteed to have optimal solutions with sufficiently long runs.

cs.DS↗