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Register a new userWhat is important about the No Free Lunch theorems?
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Added by
David Wolpert
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Authors
David H. Wolpert
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The No Free Lunch theorems prove that under a uniform distribution over induction problems (search problems or learning problems), all induction algorithms perform equally. As I discuss in this chapter, the importance of the theorems arises by using them to analyze scenarios involving {non-uniform} distributions, and to compare different algorithms, without any assumption about the distribution over problems at all. In particular, the theorems prove that {anti}-cross-validation (choosing among a set of candidate algorithms based on which has {worst} out-of-sample behavior) performs as well as cross-validation, unless one makes an assumption -- which has never been formalized -- about how the distribution over induction problems, on the one hand, is related to the set of algorithms one is choosing among using (anti-)cross validation, on the other. In addition, they establish strong caveats concerning the significance of the many results in the literature which establish the strength of a particular algorithm without assuming a particular distribution. They also motivate a ``dictionary between supervised learning and improve blackbox optimization, which allows one to ``translate techniques from supervised learning into the domain of blackbox optimization, thereby strengthening blackbox optimization algorithms. In addition to these topics, I also briefly discuss their implications for philosophy of science.
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The important recent book by G. Schurz appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior -- they prove that there are as many priors (loosely speaking) for which any induction algorithm $A$ out-generalizes some induction algorithm $B$ as vice-versa. Importantly though, in addition to the NFL theorems, there are many textit{free lunch} theorems. In particular, the NFL theorems can only be used to compare the textit{marginal} expected performance of an induction algorithm $A$ with the marginal expected performance of an induction algorithm $B$. There is a rich set of free lunches which instead concern the statistical correlations among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocate as a solution to Humes problem are just an example of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference.
Adversarial perturbations are imperceptible changes to input pixels that can change the prediction of deep learning models. Learned weights of models robust to such perturbations are previously found to be transferable across different tasks but this applies only if the model architecture for the source and target tasks is the same. Input gradients characterize how small changes at each input pixel affect the model output. Using only natural images, we show here that training a student models input gradients to match those of a robust teacher model can gain robustness close to a strong baseline that is robustly trained from scratch. Through experiments in MNIST, CIFAR-10, CIFAR-100 and Tiny-ImageNet, we show that our proposed method, input gradient adversarial matching, can transfer robustness across different tasks and even across different model architectures. This demonstrates that directly targeting the semantics of input gradients is a feasible way towards adversarial robustness.
The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained hypothesis is incorrect when presented with a random input) of a quantum learning algorithm trained via pairs of input and output states when averaged over training pairs and unitaries. The bound is illustrated using a recently introduced QNN architecture.
Microservice architecture advocates a number of technologies and practices such as lightweight container, container orchestration, and DevOps, with the promised benefits of faster delivery, improved scalability, and greater autonomy. However, microservice systems implemented in industry vary a lot in terms of adopted practices and achieved benefits, drastically different from what is advocated in the literature. In this article, we conduct an empirical study, including an online survey with 51 responses and 14 interviews for experienced microservice experts to advance our understanding regarding to microservice practices in industry. As a part of our findings, the empirical study clearly revealed three levels of maturity of microservice systems (from basic to advanced): independent development and deployment, high scalability and availability, and service ecosystem, categorized by the fulfilled benefits of microservices. We also identify 11 practical issues that constrain the microservice capabilities of organizations. For each issue, we summarize the practices that have been explored and adopted in industry, along with the remaining challenges. Our study can help practitioners better position their microservice systems and determine what infrastructures and capabilities are worth investing. Our study can also help researchers better understand industrial microservice practices and identify useful research problems.
Epigenetics has captured the attention of scientists in the past decades, yet its scope has been continuously changing. In this paper, we give an overview on how and why its definition has evolved and suggest several clarification on the concepts used in this field, in particular, on the notions of epigenetic information, epigenetic stability and epigenetic templating. Another issue that we address is the role of epigenetic information. Not only it is important in allowing alternative interpretations of genetic information, but it appears to be important in protecting the genetic information, moreover, we suggest that this function appeared first in evolution and only later on the epigenetic mechanisms were recruited to play a role in cell differentiation.
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