Economic inequality and burden-sharing in the provision of local environmental quality

By J. Cárdenas, J. Stranlund, C. Willis. 2002

5,982 citations recorded by the source corpus.

Subfields: Economics and Econometrics, General Decision Sciences, Safety Research

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In General Decision Sciences

In Safety Research

Citations in the corpus

On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization (2019, methodology): “The following useful facts are simple in matrix analysis (Horn & Johnson, 1985).”
A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks (2018, background): “Recall that for any matrices A and B of compatible sizes σmin(A + B) ≥ σmin(A) − σmax(B), and that the Frobenius norm of a matrix is always lower bounded by its largest singular value (Horn and Johnson (1990)).”
A tutorial on spectral clustering (2007, methodology): “3 of Bhatia (1997). In perturbation theory, distances between subspaces are usually measured using “canonical angles” (also called “principal angles”).”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “Returning to the graph Laplacian eigenvalues and eigenvectors, the Courant-Fischer Theorem [35, Theorem 4.2.11] tells us they can also be deﬁned iteratively via the Rayleigh quotient as and where the eigenvector u l is the minimizer of the l th problem.”
Residual Flows for Invertible Generative Modeling (2019, background): “Lastly, we emphasize that the convergence of the infinite series (3) is guaranteed for any induced matrix norm, as they still upper bound the spectral radius (Horn and Johnson, 2012).”
Accelerating the Convergence Rates of Distributed Subgradient Methods with Adaptive Quantization (2018, background): “Also, we denote by σ2 ∈ (0, 1) the second largest singular value of A, which by the Courant-Fisher theorem [11] gives ∥∥∥∥A(I− 1 n11T )∥∥∥∥ ≤ σ2 ∥∥∥∥I− 1 n11T ∥∥∥∥ .”
Learning to Relate Images (2011, background): “They can therefore also be thought of as a way to implement mapping units that encode relations.”
Excess risk bounds for multitask learning with trace norm regularization (2012, methodology): “In the sequel we will use Hoelder’s inequality [10] for linear maps in the following form.”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “, λp are the (nonnegative) eigenvalues of Q [101].”
The Singular Values of Convolutional Layers (2018, methodology): “Since the singular values of any normal matrix are the magnitudes of its eigenvalues (Horn and Johnson (2012) page 158), applying Lemma 4 completes the proof.”
Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective (2007, background): “Lemma 2 ([56]): For two positive definite matrices and , if is positive semi-definite, then .”
The graphs for which the maximum multiplicity of an eigenvalue is two (2007, background): “Note that the Schur complement (see [5], Ch.”
Concentration of the adjacency matrix and of the Laplacian in random graphs with independent edges (2009, background): “Standard eigenvalue interlacing inequalities [40] imply: This immediately implies that: Corollary 3.1 In the setting of Theorem 3.1, Therefore, the RHS holds with probability ≥ 1 δ for any and the RHS holds with probability ≥ 1 − δ for all δ as above if d ≥ C ln n .”
Rayleigh Quotient Based Optimization Methods For Eigenvalue Problems (2014, positive): “This article focuses on classes of eigenvalue problems that admit various min-max principles and the Cauchy interlacing inequalities as the symmetric eigenvalue problem famously does [4, 38, 47].”
Principal component analysis: a review and recent developments (2016, background): “the sum of squared differences with corresponding elements of Y is given [7] by Yq = UqLqAq, (2.”
Certifiably Optimal Low Rank Factor Analysis (2016, methodology): “Step 2 only relies on computing the eigenvalues of Σ − diag( u ).”
Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies (2015, background): “ndom walk with a probability transition matrix P given by P ij= P w ij j w ij : (11) By the Perron-Frobenius theorem, if P is irreducible then it has a stationary distribution ˇ which satisﬁes ˇP = ˇ [26]. One can then deﬁne the following variation functional for signals on directed graphs [27], [28”