The q-Analogue of the Extended Generalized Gamma Distribution

This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of fit is assessed by making use of the Anderson–Darling and Cram´er–von Mises criteria, among others. Improved approximations to the distribution of quadratic forms are considered as well. Since much effort was expended to develop the code required to implement the various methodologi

Learning to Guide Decoding for Image Captioning

Recently, much advance has been made in image captioning, and an encoder-decoder framework has achieved outstanding performance for this task. In this paper, we propose an extension of the encoder-decoder framework by adding a component called guiding network. The guiding network models the attribute properties of input images, and its output is leveraged to compose the input of the decoder at each time step. The guiding network can be plugged into the current encoder-decoder framework and trained in an end-to-end manner. Hence, the guiding vector can be adaptively learned according to the signal from the decoder, making itself to embed information from both image and language. Additionally, discriminative supervision can be employed to further improve the quality of guidance. The advantages of our proposed approach are verified by experiments carried out on the MS COCO dataset.Comment: AAAI-1

A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming

We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a subproblem based on a local model of infeasibility is formulated to determine a corrective step. In the second phase, a search direction that moves toward optimality is computed by minimizing a local model of the objective function. Importantly, regardless of the feasibility of the original problem, the iterative sequence generated by our proposed method converges to a Fritz-John point of a transformed problem, wherein the constraint violation is minimized. Numerical experiments have been conducted on various complex scenarios to demonstrate the effectiveness of our approach.Comment: 34 page

Allocating Divisible Resources on Arms with Unknown and Random Rewards

We consider a decision maker allocating one unit of renewable and divisible resource in each period on a number of arms. The arms have unknown and random rewards whose means are proportional to the allocated resource and whose variances are proportional to an order $b$ of the allocated resource. In particular, if the decision maker allocates resource $A_i$ to arm $i$ in a period, then the reward $Y_i$ is$Y_i(A_i)=A_i \mu_i+A_i^b \xi_{i}$, where $\mu_i$ is the unknown mean and the noise $\xi_{i}$ is independent and sub-Gaussian. When the order $b$ ranges from 0 to 1, the framework smoothly bridges the standard stochastic multi-armed bandit and online learning with full feedback. We design two algorithms that attain the optimal gap-dependent and gap-independent regret bounds for $b\in [0,1]$, and demonstrate a phase transition at $b=1/2$. The theoretical results hinge on a novel concentration inequality we have developed that bounds a linear combination of sub-Gaussian random variables whose weights are fractional, adapted to the filtration, and monotonic

Algorithmic Decision-Making Safeguarded by Human Knowledge

Commercial AI solutions provide analysts and managers with data-driven business intelligence for a wide range of decisions, such as demand forecasting and pricing. However, human analysts may have their own insights and experiences about the decision-making that is at odds with the algorithmic recommendation. In view of such a conflict, we provide a general analytical framework to study the augmentation of algorithmic decisions with human knowledge: the analyst uses the knowledge to set a guardrail by which the algorithmic decision is clipped if the algorithmic output is out of bound, and seems unreasonable. We study the conditions under which the augmentation is beneficial relative to the raw algorithmic decision. We show that when the algorithmic decision is asymptotically optimal with large data, the non-data-driven human guardrail usually provides no benefit. However, we point out three common pitfalls of the algorithmic decision: (1) lack of domain knowledge, such as the market competition, (2) model misspecification, and (3) data contamination. In these cases, even with sufficient data, the augmentation from human knowledge can still improve the performance of the algorithmic decision