Estimating the number of classes

Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds prevents the existence of locally unbiased and informative estimators and restricts confidence intervals to be one-sided. Confidence intervals for the number of classes are also necessarily one-sided. A sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classes.Comment: Published at http://dx.doi.org/10.1214/009053606000001280 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Rates of Approximation by ReLU Shallow Neural Networks

Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from H\"older spaces by these networks is crucial for understanding the efficiency of the induced learning algorithms. Although the topic has been well investigated in the setting of deep neural networks with many layers of hidden neurons, it is still open for shallow networks having only one hidden layer. In this paper, we provide rates of uniform approximation by these networks. We show that ReLU shallow neural networks with $m$ hidden neurons can uniformly approximate functions from the H\"older space $W_\infty^r([-1, 1]^d)$ with rates $O((\log m)^{\frac{1}{2} +d}m^{-\frac{r}{d}\frac{d+2}{d+4}})$ when $r<d/2 +2$. Such rates are very close to the optimal one $O(m^{-\frac{r}{d}})$ in the sense that $\frac{d+2}{d+4}$ is close to $1$, when the dimension $d$ is large

Unleashing Innovation

Using a sample of venture capital (VC)-backed initial public offering (IPO) firms, we study the effect of financial intermediaries’ tight leash on entrepreneurs’ innovation productivity. We find that financial intermediaries’ tight leash impedes innovation: IPO firms are significantly less innovative when VCs interfere with their development more frequently through staging—as measured by a larger number of VC financing rounds. To establish causality, we exploit plausibly exogenous variation in the frequency of direct flights between VC domiciles and IPO firm headquarters that are due to airline restructuring. Our identification tests suggest a negative, causal effect of VC staging on firm innovation. Furthermore, staging is more detrimental to innovation when innovation is more difficult to achieve and when VCs are less experienced with the industry in which their entrepreneurial firms operate. By documenting a previously underrecognized adverse consequence of VC stage financing, our evidence suggests that contract mechanisms are at play so that short-termist incentives can be cultivated even in a private equity market populated with long-term, sophisticated investors

Branching ratio and CPCP violation of B→KπB\to K\pi decays in a modified perturbative QCD approach

We calculate the branching ratio and $CP$ violations for $B\to K\pi$ decays in a modified perturbative QCD approach based on $k_{T}$ factorization. The resummation effect of the transverse momentum regulates the endpoint singularity. Using the $B$ meson wave function that is obtained in the relativistic potential model, soft contribution cannot be suppressed effectively by Sudakov factor. Soft scale cutoff and soft $BK$, $B\pi$ and $K\pi$ form factors have to be introduced. The most important next-to-leading-order contributions from the vertex corrections, the quark loops, and the magnetic penguins are also considered. In addition, the contribution of the color-octet hadronic matrix element is included which is essentially of long-distance dynamics. Our predictions for branching ratios and $CP$ violations are in good agreement with the experimental data. Especially the theoretical result of dramatic difference between the $CP$ violations of $B^+\to K^+\pi^0$ and $B^0\to K^+\pi^-$ is consistent with experimental measurement, therefore the $K\pi$ puzzle in $B$ decays can be resolved in our way of the modified perturbative QCD approach.Comment: 19 pages, 2 figures, version to appear in Phys. Rev.

A WOA-based optimization approach for task scheduling in cloud Computing systems

Task scheduling in cloud computing can directly affect the resource usage and operational cost of a system. To improve the efficiency of task executions in a cloud, various metaheuristic algorithms, as well as their variations, have been proposed to optimize the scheduling. In this work, for the first time, we apply the latest metaheuristics WOA (the whale optimization algorithm) for cloud task scheduling with a multiobjective optimization model, aiming at improving the performance of a cloud system with given computing resources. On that basis, we propose an advanced approach called IWC (Improved WOA for Cloud task scheduling) to further improve the optimal solution search capability of the WOA-based method. We present the detailed implementation of IWC and our simulation-based experiments show that the proposed IWC has better convergence speed and accuracy in searching for the optimal task scheduling plans, compared to the current metaheuristic algorithms. Moreover, it can also achieve better performance on system resource utilization, in the presence of both small and large-scale tasks

The Role of Human Capital: Evidence From Patent Generation

Firms exhibit persistence in innovation output. This paper focuses on the role played by individual inventors. Compared to firm organizational capital, human capital embedded in inventors explains a majority of the variation in innovation performance but much less in innovation style. Inventors contribute more when they are better networked, in firms with higher inventor mobility, and in industries in which innovation is more difficult. Additional tests suggest that our main findings are unlikely driven by inventors’ endogenous moving. This paper highlights the importance of human capital in enhancing firm innovation and sheds new light on the theory of the firm

Do Individuals or Firms Matter More? The Case of Patent Generation

This paper studies the relative importance of individual inventors’ human capital and firms’ organizational capital in promoting a firm’s innovation output. We decompose the variation in innovation output into inventor- and firm-specific components. Inventors’ human capital is about 13 times as important as firms’ organizational capital in explaining a firm’s innovation performance in terms of patent counts and citations, while inventors’ human capital is only about the same as important when explaining the firm’s innovation styles in terms of patent exploratory and exploitive scores. In the cross section, inventors contribute more to innovation output when they are better networked, in firms with higher inventor mobility, in industries in which innovation is more difficult to achieve, and in publicly traded firms. Additional tests suggest that our main findings continue to hold after accounting for inventors’ endogenous moving. This paper highlights the importance of individual inventors in enhancing firm innovation and sheds new light on the theory of the firm

Hubris or Talent? Estimating the Role of Overconfidence in Chinese households’ Investment Decisions

We document the extent to which overconfidence in one’s financial literacy (FL overconfidence) plays a role in households’ reported financial risk aversion and their actual investment behavior, using data from the China Household Finance Survey. We measure FL overconfidence by estimating the gap between people’s self-reported financial literacy and their objectively measured financial knowledge. Our results indicate that FL overconfidence is negatively associated with self-reported financial risk aversion. Additionally, FL overconfidence is positively associated with the likelihood of having a brokerage account, holding risky financial instruments (other than just stock), and a proportion of assets allocated towards risky assets. We then use machine learning methods to predict which factors are most important in determining households’ risky investment decisions. We find that overconfidence plays a significant predictive role. Our work signals that households’ risky investments may be driven by biased optimism about their own financial know-how rather than their actual knowledge. We conclude that financial literacy programs should not only teach financial concepts but also make program participants aware of their own biases