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Rounding SumofSquares Relaxations
, 2014
"... We present a general approach to rounding semidefinite programming relaxations obtained by the SumofSquares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the SumofSquares proof system to transform a combining algorithm—an algorithm that ..."
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Cited by 8 (0 self)
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We present a general approach to rounding semidefinite programming relaxations obtained by the SumofSquares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the SumofSquares proof system to transform a combining algorithm—an algorithm
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N = 2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira– Spencer theory, which may be viewed as the closed string analog of the Chern–Simon theory. Using the mirror map this leads to computation of the ‘number ’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2 theory. Relations with c = 1 strings are also pointed out.
Dictionary Learning and Tensor Decomposition via the SumofSquares Method
, 2014
"... We give a new approach to the dictionary learning (also known as “sparse coding”) problem of recovering an unknown n × m matrix A (for m> n) from examples of the form y = Ax + e, where x is a random vector in Rm with at most τm nonzero coordinates, and e is a random noise vector in Rn with bounde ..."
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Cited by 2 (0 self)
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there is no guarantee that the local optima of T and T ′ have similar structures. Our algorithm is based on a novel approach to using and analyzing the Sum of Squares semidefinite programming hierarchy (Parrilo 2000, Lasserre 2001), and it can be viewed as an indication of the utility of this very general and powerful
Hypercontractivity, SumofSquares Proofs, and their Applications
, 2013
"... We study the computational complexity of approximating the 2toq norm of linear operators (defined as ‖A‖2→q = maxv�0‖Av‖q/‖v‖2) for q> 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot’s Unique Games Conjecture (UGC). We show ..."
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close variant of the UGC. We also show that such a good approximation can be computed in exp(n 2/q) time, thus obtaining a different proof of the known subexponential algorithm for SmallSet Expansion. 2. Constant rounds of the “Sum of Squares ” semidefinite programing hierarchy certify an upper bound
Noncommutative circuits and the sumofsquares problem
 J. Amer. Math. Soc
"... 1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of ..."
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Cited by 2 (2 self)
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1.1. Noncommutative computation. Arithmetic complexity theory studies the computation of formal polynomials over some field or ring. Most of this theory is concerned with the computation of commutative polynomials. The basic model of computation is that of an arithmetic circuit. Despite decades of work, the best
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
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Cited by 548 (13 self)
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, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where
On the SumofSquares Algorithm for Bin Packing
, 2000
"... In this paper we present a theoretical analysis of the deterministic online Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s(a) ar ..."
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Cited by 126 (6 self)
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In this paper we present a theoretical analysis of the deterministic online Sum of Squares algorithm (SS) for bin packing, introduced and studied experimentally in [8], along with several new variants. SS is applicable to any instance of bin packing in which the bin capacity B and item sizes s
Regression Shrinkage and Selection Via the Lasso
 Journal of the Royal Statistical Society, Series B
, 1994
"... We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactl ..."
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Cited by 4055 (51 self)
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We propose a new method for estimation in linear models. The "lasso" minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 973 (4 self)
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. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums
Results 1  10
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