In the strategic management theory, the structure-based view holds that the structural characteristic of the industry is the main determinant of the performance; while the resource-based view claims that the competitive advantage is driven by the resource and capacity of an enterprise. In this paper, we carry out an empirical research on 945 Chinese listed companies’ performance (ROA) in 18 ind...

The seller of a contingent claim H can always find a self-financing investment strategy that (super)hedges the claim H. When the seller wants to endow an initial capital x less than the one required to get perfect (super)hedging, the shortfall risk minimisation problem arises in a natural way. The aim is to find the strategy that minimises E{`([H(ST )−V x,φ T ])} (shortfall risk), where V x,φ t...

In stochastic convex optimization the goal is to minimize a convex function F (x) . = Ef∼D[f(x)] over a convex set K ⊂ R where D is some unknown distribution and each f(·) in the support of D is convex over K. The optimization is commonly based on i.i.d. samples f, f, . . . , f from D. A standard approach to such problems is empirical risk minimization (ERM) that optimizes FS(x) . = 1 n ∑ i≤n f...

In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing compositions of convex functions and smooth maps, and Catalyst generic acceleration for regularized Empirical Risk Minimization.

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many loss functions besides the squared loss, and scales only with the sub-Gaussian or subexponential parameters without further statistical assumptions such as the...

The theoretical framework of Statistical Learning Theory (SLT) for pattern recognition problems is extended to comprehend the situations where an infinite value of the loss function is employed to prevent misclassifications in specific regions with high reliability. Sufficient conditions for ensuring the consistency of the Empirical Risk Minimization (ERM) criterion are then established and an ...

We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all local curvature information contained in the examples, which leads to striking impr...

We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. For strongly convex functions, our method achiev...

We consider the problem of training a conditional random field (CRF) to maximize per-label predictive accuracy on a training set, an approach motivated by the principle of empirical risk minimization. We give a gradient-based procedure for minimizing an arbitrarily accurate approximation of the empirical risk under a Hamming loss function. In experiments with both simulated and real data, our o...