计量经济分析 = Econometric analysis

‘The Production of Space’, in: Frans Jacobi, Imagine, Space Poetry, Copenhagen, 1996, unpaginated.

The Production of Space

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Convex Analysisの二,三の進展について

The Structural Transformation of the Public Sphere: An Inquiry into a Category of Bourgeois Society

On robust estimation of the location parameter

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

In this paper, we describe the embedded conic solver (ECOS), an interior-point solver for second-order cone programming (SOCP) designed specifically for embedded applications. ECOS is written in low footprint, single-threaded, library-free ANSI-C and so runs on most embedded platforms. The main interior-point algorithm is a standard primal-dual Mehrotra predictor-corrector method with Nesterov-Todd scaling and self-dual embedding, with search directions found via a symmetric indefinite KKT system, chosen to allow stable factorization with a fixed pivoting order. The indefinite system is solved using Davis' SparseLDL package, which we modify by adding dynamic regularization and iterative refinement for stability and reliability, as is done in the CVXGEN code generation system, allowing us to avoid all numerical pivoting; the elimination ordering is found entirely symbolically. This keeps the solver simple, only 750 lines of code, with virtually no variation in run time. For small problems, ECOS is faster than most existing SOCP solvers; it is still competitive for medium-sized problems up to tens of thousands of variables.

/pdf/ecos-an-socp-solver-for-embedded-systems-35wspce41g.pdf

ECOS: An SOCP solver for embedded systems

We introduce a first-order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent feasibility problem involving finding a nonzero point in the intersection of a subspace and a cone. This approach has several favorable properties. Compared to interior-point methods, first-order methods scale to very large problems, at the cost of requiring more time to reach very high accuracy. Compared to other first-order methods for cone programs, our approach finds both primal and dual solutions when available or a certificate of infeasibility or unboundedness otherwise, is parameter free, and the per-iteration cost of the method is the same as applying a splitting method to the primal or dual alone. We discuss efficient implementation of the method in detail, including direct and indirect methods for computing projection onto the subspace, scaling the original problem data, and stopping criteria. We describe an open-source implementation, which handles the usual (symmetric) nonnegative, second-order, and semidefinite cones as well as the (non-self-dual) exponential and power cones and their duals. We report numerical results that show speedups over interior-point cone solvers for large problems, and scaling to very large general cone programs.

/pdf/conic-optimization-via-operator-splitting-and-homogeneous-1fxr7pcmul.pdf

Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding

Adaptation needs and options

The 2015 United Nations Climate Change Conference in Paris (COP21) highlighted the importance of cities to climate action, as well as the unjust burdens borne by the world's most disadvantaged peoples in addressing climate impacts. Few studies have documented the barriers to redressing the drivers of social vulnerability as part of urban local climate change adaptation efforts, or evaluated how emerging adaptation plans impact marginalized groups. Here, we present a roadmap to reorient research on the social dimensions of urban climate adaptation around four issues of equity and justice: (1) broadening participation in adaptation planning; (2) expanding adaptation to rapidly growing cities and those with low financial or institutional capacity; (3) adopting a multilevel and multi-scalar approach to adaptation planning; and (4) integrating justice into infrastructure and urban design processes. Responding to these empirical and theoretical research needs is the first step towards identifying pathways to more transformative adaptation policies.

/pdf/roadmap-towards-justice-in-urban-climate-adaptation-research-1bxrrn1up7.pdf

Eric Chu

Papers

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

ECOS: An SOCP solver for embedded systems

Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding

Adaptation needs and options

Roadmap towards justice in urban climate adaptation research