Data Dependence Vectors Research Articles

Inference after estimation of breaks

In an important class of econometric problems, researchers select a target parameter by maximizing the Euclidean norm of a data-dependent vector. Examples that can be cast into this frame include threshold regression models with estimated thresholds and structural break models with estimated break dates. Estimation and inference procedures that ignore the randomness of the target parameter can be severely biased and misleading when this randomness is non-negligible. This paper studies conditional and unconditional inference in such settings, accounting for the data-dependent choice of target parameters. We detail the construction of quantile-unbiased estimators and confidence sets with correct coverage, and prove their asymptotic validity under data generating process such that the target parameter remains random in the limit. We also provide a novel sample splitting approach that improves on conventional split-sample inference.

PAC-Bayes analysis of multi-view learning

Multi-view learning is a widely applicable research direction. This paper presents eight PAC-Bayes bounds to analyze the generalization performance of multi-view classifiers. These bounds adopt data dependent Gaussian priors which emphasize classifiers with high view agreements. The center of the prior for the first two bounds is the origin, while the center of the prior for the third and fourth bounds is given by a data dependent vector. An important technique to obtain these bounds is two derived logarithmic determinant inequalities whose difference lies in whether the dimensionality of data is involved. The centers of the fifth and sixth bounds are calculated on a separate subset of the training set. The last two bounds use unlabeled data to represent view agreements and are thus applicable to semi-supervised multi-view learning. We evaluate all the presented multi-view PAC-Bayes bounds on benchmark data and compare them with previous single-view PAC-Bayes bounds. The usefulness and performance of the multi-view bounds are discussed.

Maximizing parallelism and minimizing synchronization with affine partitions

This paper presents an algorithm to find the optimal affine partitions that maximize the degree of parallelism and minimize the degree of synchronization in programs with arbitrary loop nestings and affine data accesses. The problem is formulated without the use of imprecise data dependence abstractions such as data dependence vectors. The algorithm presented subsumes previously proposed loop transformation algorithms that are based on unimodular transformations, loop distribution, fusion, scaling, reindexing, and statement reordering.

A NEW APPROACH TO FINDING OPTIMAL LINEAR SCHEDULES FOR UNIFORM DEPENDENCE ALGORITHMS†

A uniform dependence algorithm can be represented by an index set of index points and a finite set of data dependence vectors. Usually, the convex hull R of the index set is a nondegenerated convex polytope in R n, In this paper, we show that finding an optimal linear schedule for a uniform dependence algorithm with an arbitrary bounded convex index set is equivalent to finding a vector of smallest norm, where the vector norm is defined on a symmetric convex set R∗ (which is the dual of difference body R − R). A linear programming problem is derived for finding the smallest vector. This problem can be solved in the empirical average time complexity O(36n 3 + 12an 2 + a), where a is the number of the linear inequalities defining the convex hull R and n is the dimension of the index set. This time complexity is better than those of the existing methods.

Solving linear systems of equations

The mapping of p-nested loop algorithms into special-purpose VLSI arrays is based on the linear transformations of index sets and data dependence vectors. The problem of synchronizing a sequence of parallel algorithms is also considered. Implementations for complete solving of a linear system of equations with LU decomposition for symmetric positive definite matrices are shown.

On the design of algorithms for VLSI systolic arrays

This paper is concerned with the mapping of cyclic loop algorithms into special-purpose VLSI arrays. The mapping procedure is based on the mathematical transformations of index sets and data dependence vectors. Necessary and sufficient conditions for the existence of valid transformations are given for algorithms with constant data dependences. Two examples of different algorithms are given to illustrate the proposed mapping procedure; first is the LU decomposition of a matrix which leads to constant data dependence vectors, and secondly is the dynamic programming which leads to dependences which are functions on the index set and are more difficult to be mapped into VLSI arrays.

Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem

A decentralized control problem involving K nodes is formulated At each node are sensors and controls. The object is to share the information of each sensor, processed with a local Kalman estimator, with all the other nodes so that the controllers can be computed using the best estimate of the state of the system given the information from all the sensors. The controls are determined so that the expected value of a quadratic performance index is minimized. The problem is formulated as a decentralized control problem without a central supervisor so that the system performance will degrade gracefully under structural perturbations. Therefore, the transmission of data is from each node to every other node; there are \sum\liminf{i-1}\limsup{k}(i-1) links connecting all nodes. It is shown that if the dimension of the controls at each node l is less than both the dimension of the data at node m and the dimension of the state, then a data vector with dimension of the control at l can be transmitted from m to l . compression of data transmission is done at the expense of propagating an additionaal data dependent vector at each node beyond the usual Kalman filter equations.