196,304 research outputs found
An Almost Optimal Algorithm for Computing Nonnegative Rank
No full textHere, we give an algorithm for deciding if the nonnegative rank of a matrix M of dimension m \times n$ is at most r which runs in time (nm)[superscript O(r2)]. This is the first exact algorithm that runs in time singly exponential in r. This algorithm (and earlier algorithms) are built on methods for finding a solution to a system of polynomial inequalities (if one exists). Notably, the best algorithms for this task run in time exponential in the number of variables but polynomial in all of the other parameters (the number of inequalities and the maximum degree). Hence, these algorithms motivate natural algebraic questions whose solution have immediate algorithmic implications: How many variables do we need to represent the decision problem, and does M have nonnegative rank at most r? A naive formulation uses nr + mr variables and yields an algorithm that is exponential in n and m even for constant r. Arora et al. [Proceedings of STOC, 2012, pp. 145--162] recently reduced the number of variables to 2r[superscript 2] 2[superscript r], and here we exponentially reduce the number of variables to 2r[superscript 2] and this yields our main algorithm. In fact, the algorithm that we obtain is nearly optimal (under the exponential time hypothesis) since an algorithm that runs in time (nm)[superscript o(r)] would yield a subexponential algorithm for 3-SAT [Proceedings of STOC, 2012, pp. 145--162]. Our main result is based on establishing a normal form for nonnegative matrix factorization---which in turn allows us to exploit algebraic dependence among a large collection of linear transformations with variable entries. Additionally, we also demonstrate that nonnegative rank cannot be certified by even a very large submatrix of M, and this property also follows from the intuition gained from viewing nonnegative rank through the lens of systems of polynomial inequalities.National Science Foundation (U.S.) (Computing and Innovation Fellowship)National Science Foundation (U.S.) (grant DMS-0835373
Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices
No full textSuper-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency (m) and the
separation (∆). If m > 1/∆ + 1, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when m < (1 − epsilon )/∆ no estimator can distinguish between a particular pair of ∆-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between extremal functions and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in
turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing
Historical Cultures under Conditions of Deindustrialization Working Group Report
No full textCrumbling smokestacks, shuttered furnaces, and abandoned quarries are all striking representations of deindustrialization. These and other images construct a discourse whose ideological undertones, far from confining them to the realm of symbolic nostalgia, have profound effects on contemporary societies. In 2015, within the European Labor History Network (ELHN), a working group on historical cultures of labor under conditions of deindustrialization (working group) began to critically study and reflect on this nascent theme. It grew from a small group of researchers to a network of academics across Europe and beyond. Though the study of deindustrialization is not new, contemporary work offers insights into the continuing struggle over the meaning of classical industrial work and its loss, revealing unresolved social, cultural, and political tensions. Yet, existing representations of deindustrialization have been criticized as “smokestack nostalgia.” In order to chart how we understand contemporary industrial decay in our political, cultural, and economic climate, the working group explores representations and more-than representations of loss and regeneration in deindustrialized regions, primarily in Europe but widening to include a growing global network
Noisy Tensor Completion via the Sum-of-Squares Hierarchy
No full text© 2016 B. Barak & A. Moitra. In the noisy tensor completion problem we observe m entries (whose location is chosen uniformly at random) from an unknown n1 × n2 × n3 tensor T. We assume that T is entry-wise close to being rank r. Our goal is to fill in its missing entries using as few observations as possible. Let n = max(n1, n2, n3). We show that if m = n3/2r then there is a polynomial time algorithm based on the sixth level of the sum-of-squares hierarchy for completing it. Our estimate agrees with almost all of T's entries almost exactly and works even when our observations are corrupted by noise. This is also the first algorithm for tensor completion that works in the overcomplete case when r > n, and in fact it works all the way up to r = n3/2−ε . Our proofs are short and simple and are based on establishing a new connection between noisy tensor completion (through the language of Rademacher complexity) and the task of refuting random constant satisfaction problems. This connection seems to have gone unnoticed even in the context of matrix completion. Furthermore, we use this connection to show matching lower bounds. Our main technical result is in characterizing the Rademacher complexity of the sequence of norms that arise in the sum-of-squares relaxations to the tensor nuclear norm. These results point to an interesting new direction: Can we explore computational vs. sample complexity tradeoffs through the sum-of-squares hierarchy
Vertex sparsifiers : new results from old techniques
No full textGiven a capacitated graph and a set of terminals , how should we produce a graph only on the terminals so that every (multicommodity) flow between the terminals in could be supported in with low congestion, and vice versa? (Such a graph is called a flow sparsifier for .) What if we want to be a “simple” graph? What if we allow to be a convex combination of simple graphs? Improving on results of Moitra [Proceedings of the 50th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 2009, pp. 3--12] and Leighton and Moitra [Proceedings of the 42nd ACM Symposium on Theory of Computing, ACM, New York, 2010, pp. 47--56], we give efficient algorithms for constructing (a) a flow sparsifier that maintains congestion up to a factor of , where ; (b) a convex combination of trees over the terminals that maintains congestion up to a factor of ; (c) for a planar graph , a convex combination of planar graphs that maintains congestion up to a constant factor. This requires us to give a new algorithm for the 0-extension problem, the first one in which the preimages of each terminal are connected in . Moreover, this result extends to minor-closed families of graphs. Our bounds immediately imply improved approximation guarantees for several terminal-based cut and ordering problems
New algorithms for learning incoherent and overcomplete dictionaries
No full textIn sparse recovery we are given a matrix A∈R[superscript n×m] (“the dictionary”) and a vector of the form AX where X is sparse, and the goal is to recover X. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, the dictionary A is unknown and has to be learned from random examples of the form Y=AX where X is drawn from an appropriate distribution — this is the dictionary learning problem. In most settings, A is overcomplete: it has more columns than rows. This paper presents a polynomial-time algorithm for learning overcomplete dictionaries; the only previously known algorithm with provable guarantees is the recent work of Spielman et al. (2012) who gave an algorithm for the undercomplete case, which is rarely the case in applications. Our algorithm applies to incoherent dictionaries which have been a central object of study since they were introduced in seminal work of Donoho and Huo (1999). In particular, a dictionary is μ-incoherent if each pair of columns has inner product at most μ/√n. The algorithm makes natural stochastic assumptions about the unknown sparse vector X, which can contain k≤cmin(√/n/μlogn,m[superscript 1/2−η]) non-zero entries (for any η>0). This is close to the best k allowable by the best sparse recovery algorithms even if one knows the dictionary A exactly. Moreover, both the running time and sample complexity depend on log1/ϵ, where ϵ is the target accuracy, and so our algorithms converge very quickly to the true dictionary. Our algorithm can also tolerate substantial amounts of noise provided it is incoherent with respect to the dictionary (e.g., Gaussian). In the noisy setting, our running time and sample complexity depend polynomially on 1/ϵ, and this is necessary.National Science Foundation (U.S.) (Grant DMS-0835373)National Science Foundation (U.S.) (Computing and Innovation Fellowship
Dr. Duane M. Jackson, Morehouse College, July 2011
No full textThis video is a conversation with Dr. Duane M. Jackson. Dr. Jackson talks about his paper, "Recall and the Serial Position Effect: The Role of Primacy and Recency on Accounting Students' Performance." Jackie Daniel, AUC Woodruff Library, is the interviewer
"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States" By M. Carey.
No full text"Reflections on the subject of Emigration from Europe with a view to Settlement in the United States: containing bried sketches of the moral and political character of those states.
By M. Carey, member of the American philosophical, and of the American Antiquarian Society, and author of The Olive Branch, Cindiciae Hibernicae, essays on banking, on political economy, and on internal improvement.
To which are now added the English editor's comments on the subject; together with Important Advice to Emigrants, and Cautions Against Impositions Practiced in the Outports
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Dr. Glendon Swarthout
No full textHosted by Roger M. Busfield, MSU Assistant Professor of Speech and Theater, Meet the Author is designed to introduce a general audience to a contemporary author and their work through in-depth interviews. This episode features a conversation between Dr. Glendon Swarthout, prolific author and English professor at MSU, and assistant professors Sam S. Baskett and Theodore B. Strandness
- …
