“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

Indoor localization has recently witnessed an increase in interest, due to the potential wide range of services it can provide by leveraging Internet of Things (IoT), and ubiquitous connectivity. Different techniques, wireless technologies and mechanisms have been proposed in the literature to provide indoor localization services in order to improve the services provided to the users. However, there is a lack of an up-to-date survey paper that incorporates some of the recently proposed accurate and reliable localization systems. In this paper, we aim to provide a detailed survey of different indoor localization techniques, such as angle of arrival (AoA), time of flight (ToF), return time of flight (RTOF), and received signal strength (RSS); based on technologies, such as WiFi, radio frequency identification device (RFID), ultra wideband (UWB), Bluetooth, and systems that have been proposed in the literature. This paper primarily discusses localization and positioning of human users and their devices. We highlight the strengths of the existing systems proposed in the literature. In contrast with the existing surveys, we also evaluate different systems from the perspective of energy efficiency, availability, cost, reception range, latency, scalability, and tracking accuracy. Rather than comparing the technologies or techniques, we compare the localization systems and summarize their working principle. We also discuss remaining challenges to accurate indoor localization.

A Survey of Indoor Localization Systems and Technologies

When building a unified vision system or gradually adding new capabilities to a system, the usual assumption is that training data for all tasks is always available. However, as the number of tasks grows, storing and retraining on such data becomes infeasible. A new problem arises where we add new capabilities to a Convolutional Neural Network (CNN), but the training data for its existing capabilities are unavailable. We propose our Learning without Forgetting method, which uses only new task data to train the network while preserving the original capabilities. Our method performs favorably compared to commonly used feature extraction and fine-tuning adaption techniques and performs similarly to multitask learning that uses original task data we assume unavailable. A more surprising observation is that Learning without Forgetting may be able to replace fine-tuning with similar old and new task datasets for improved new task performance.

Learning without Forgetting

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision, and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this paper is to provide a comprehensive study and an updated review on sparse representation and to supply guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: 1) sparse representation with $l_{0}$ -norm minimization; 2) sparse representation with $l_{p}$ -norm ( $0 ) minimization; 3) sparse representation with $l_{1}$ -norm minimization; 4) sparse representation with $l_{2,1}$ -norm minimization; and 5) sparse representation with $l_{2}$ -norm minimization. In this paper, a comprehensive overview of sparse representation is provided. The available sparse representation algorithms can also be empirically categorized into four groups: 1) greedy strategy approximation; 2) constrained optimization; 3) proximity algorithm-based optimization; and 4) homotopy algorithm-based sparse representation. The rationales of different algorithms in each category are analyzed and a wide range of sparse representation applications are summarized, which could sufficiently reveal the potential nature of the sparse representation theory. In particular, an experimentally comparative study of these sparse representation algorithms was presented.

A Survey of Sparse Representation: Algorithms and Applications

The special importance of L1/2 regularization has been recognized in recent studies on sparse modeling (particularly on compressed sensing). The L1/2 regularization, however, leads to a nonconvex, nonsmooth, and non-Lipschitz optimization problem that is difficult to solve fast and efficiently. In this paper, through developing a threshoding representation theory for L1/2 regularization, we propose an iterative half thresholding algorithm for fast solution of L1/2 regularization, corresponding to the well-known iterative soft thresholding algorithm for L1 regularization, and the iterative hard thresholding algorithm for L0 regularization. We prove the existence of the resolvent of gradient of ||x||1/21/2, calculate its analytic expression, and establish an alternative feature theorem on solutions of L1/2 regularization, based on which a thresholding representation of solutions of L1/2 regularization is derived and an optimal regularization parameter setting rule is formulated. The developed theory provides a successful practice of extension of the well- known Moreau's proximity forward-backward splitting theory to the L1/2 regularization case. We verify the convergence of the iterative half thresholding algorithm and provide a series of experiments to assess performance of the algorithm. The experiments show that the half algorithm is effective, efficient, and can be accepted as a fast solver for L1/2 regularization. With the new algorithm, we conduct a phase diagram study to further demonstrate the superiority of L1/2 regularization over L1 regularization.

$L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver

In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $$\phi (x_0,\ldots ,x_p,y)$$
 , subject to coupled linear equality constraints. Our ADMM updates each of the primal variables $$x_0,\ldots ,x_p,y$$
 , followed by updating the dual variable. We separate the variable y from $$x_i$$
 ’s as it has a special role in our analysis. The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, $$\ell _q$$
 quasi-norm, Schatten-q quasi-norm (
 $$0<q<1$$
 ), minimax concave penalty (MCP), and smoothly clipped absolute deviation penalty. It also allows nonconvex constraints such as compact manifolds (e.g., spherical, Stiefel, and Grassman manifolds) and linear complementarity constraints. Also, the $$x_0$$
 -block can be almost any lower semi-continuous function. By applying our analysis, we show, for the first time, that several ADMM algorithms applied to solve nonconvex models in statistical learning, optimization on manifold, and matrix decomposition are guaranteed to converge. Our results provide sufficient conditions for ADMM to converge on (convex or nonconvex) monotropic programs with three or more blocks, as they are special cases of our model. ADMM has been regarded as a variant to the augmented Lagrangian method (ALM). We present a simple example to illustrate how ADMM converges but ALM diverges with bounded penalty parameter $$\beta $$
 . Indicated by this example and other analysis in this paper, ADMM might be a better choice than ALM for some nonconvex nonsmooth problems, because ADMM is not only easier to implement, it is also more likely to converge for the concerned scenarios.

http://www.optimization-online.org/DB_FILE/2015/11/5222.pdf

Global Convergence of ADMM in Nonconvex Nonsmooth Optimization

In this paper, we analyze the convergence of the alternating direction method of multipliers (ADMM) for minimizing a nonconvex and possibly nonsmooth objective function, $\phi(x_0,\ldots,x_p,y)$, subject to coupled linear equality constraints. Our ADMM updates each of the primal variables $x_0,\ldots,x_p,y$, followed by updating the dual variable. We separate the variable $y$ from $x_i$'s as it has a special role in our analysis. 
The developed convergence guarantee covers a variety of nonconvex functions such as piecewise linear functions, $\ell_q$ quasi-norm, Schatten-$q$ quasi-norm ($0<q<1$), minimax concave penalty (MCP), and smoothly clipped absolute deviation (SCAD) penalty. It also allows nonconvex constraints such as compact manifolds (e.g., spherical, Stiefel, and Grassman manifolds) and linear complementarity constraints. Also, the $x_0$-block can be almost any lower semi-continuous function. 
By applying our analysis, we show, for the first time, that several ADMM algorithms applied to solve nonconvex models in statistical learning, optimization on manifold, and matrix decomposition are guaranteed to converge. 
Our results provide sufficient conditions for ADMM to converge on (convex or nonconvex) monotropic programs with three or more blocks, as they are special cases of our model. 
ADMM has been regarded as a variant to the augmented Lagrangian method (ALM). We present a simple example to illustrate how ADMM converges but ALM diverges with bounded penalty parameter $\beta$. Indicated by this example and other analysis in this paper, ADMM might be a better choice than ALM for some nonconvex \emph{nonsmooth} problems, because ADMM is not only easier to implement, it is also more likely to converge for the concerned scenarios.

In recent studies on sparse modeling, the nonconvex regularization approaches (particularly, Lq regularization with q ∈ (0,1)) have been demonstrated to possess capability of gaining much benefit in sparsity-inducing and efficiency. As compared with the convex regularization approaches (say, L1 regularization), however, the convergence issue of the corresponding algorithms are more difficult to tackle. In this paper, we deal with this difficult issue for a specific but typical nonconvex regularization scheme, the L1/2 regularization, which has been successfully used to many applications. More specifically, we study the convergence of the iterative half thresholding algorithm (the half algorithm for short), one of the most efficient and important algorithms for solution to the L1/2 regularization. As the main result, we show that under certain conditions, the half algorithm converges to a local minimizer of the L1/2 regularization, with an eventually linear convergence rate. The established result provides a theoretical guarantee for a wide range of applications of the half algorithm. We provide also a set of simulations to support the correctness of theoretical assertions and compare the time efficiency of the half algorithm with other known typical algorithms forL1/2 regularization like the iteratively reweighted least squares (IRLS) algorithm and the iteratively reweighted l1 minimization (IRL1) algorithm.

$L_{1/2}$ Regularization: Convergence of Iterative Half Thresholding Algorithm

Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for convex consensus optimization. However, to the behaviors or consensus nonconvex optimization, our understanding is more limited. When we lose convexity, we cannot hope that our algorithms always return global solutions though they sometimes still do. Somewhat surprisingly, the decentralized consensus algorithms, DGD and Prox-DGD, retain most other properties that are known in the convex setting. In particular, when diminishing (or constant) step sizes are used, we can prove convergence to a (or a neighborhood of) consensus stationary solution under some regular assumptions. It is worth noting that Prox-DGD can handle nonconvex nonsmooth functions if their proximal operators can be computed. Such functions include SCAD, MCP, and $\ell _q$ quasi-norms, $q\in [0,1)$ . Similarly, Prox-DGD can take the constraint to a nonconvex set with an easy projection. To establish these properties, we have to introduce a completely different line of analysis, as well as modify existing proofs that were used in the convex setting.

On Nonconvex Decentralized Gradient Descent

In this note, we extend the algorithms Extra and subgradient-push to a new algorithm ExtraPush for consensus optimization with convex differentiable objective functions over a directed network. When the stationary distribution of the network can be computed in advance}, we propose a simplified algorithm called Normalized ExtraPush. Just like Extra, both ExtraPush and Normalized ExtraPush can iterate with a fixed step size. But unlike Extra, they can take a column-stochastic mixing matrix, which is not necessarily doubly stochastic. Therefore, they remove the undirected-network restriction of Extra. Subgradient-push, while also works for directed networks, is slower on the same type of problem because it must use a sequence of diminishing step sizes. 
We present preliminary analysis for ExtraPush under a bounded sequence assumption. For Normalized ExtraPush, we show that it naturally produces a bounded, linearly convergent sequence provided that the objective function is strongly convex. 
In our numerical experiments, ExtraPush and Normalized ExtraPush performed similarly well. They are significantly faster than subgradient-push, even when we hand-optimize the step sizes for the latter.

Jinshan Zeng

Papers

Global Convergence of ADMM in Nonconvex Nonsmooth Optimization

Global Convergence of ADMM in Nonconvex Nonsmooth Optimization

$L_{1/2}$ Regularization: Convergence of Iterative Half Thresholding Algorithm

On Nonconvex Decentralized Gradient Descent

ExtraPush for Convex Smooth Decentralized Optimization over Directed Networks