Changepoint Problem in Quantumn Setting

In the changepoint problem, we determine when the distribution observed has changed to another one. We expand this problem to the quantum case where copies of an unknown pure state are being distributed. We study the fundamental case, which has only two candidates to choose. This problem is equal to identifying a given state with one of the two unknown states when multiple copies of the states are provided. In this paper, we assume that two candidate states are distributed independently and uniformly in the space of the whole pure states. The minimum of the averaged error probability is given and the optimal POVM is defined as to obtain it. Using this POVM, we also compute the error probability which depends on the inner product. These analytical results allow us to calculate the value in the asymptotic case, where this problem approaches to the usual discrimination problem

Convergence rate of the (1+1)-evolution strategy on locally strongly convex functions with lipschitz continuous gradient and their monotonic transformations

Evolution strategy (ES) is one of promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on the speed of its convergence is limited on convex quadratic functions and their monotonic transformation. In this study, an upper bound and a lower bound of the rate of linear convergence of the (1+1)-ES on locally $L$-strongly convex functions with $U$-Lipschitz continuous gradient are derived as $\exp\left(-\Omega_{d\to\infty}\left(\frac{L}{d\cdot U}\right)\right)$ and $\exp\left(-\frac1d\right)$, respectively. Notably, any prior knowledge on the mathematical properties of the objective function such as Lipschitz constant is not given to the algorithm, whereas the existing analyses of derivative-free optimization algorithms require them.Comment: 15 page

CAMRI Loss: Improving Recall of a Specific Class without Sacrificing Accuracy

In real-world applications of multi-class classification models, misclassification in an important class (e.g., stop sign) can be significantly more harmful than in other classes (e.g., speed limit). In this paper, we propose a loss function that can improve the recall of an important class while maintaining the same level of accuracy as the case using cross-entropy loss. For our purpose, we need to make the separation of the important class better than the other classes. However, existing methods that give a class-sensitive penalty for cross-entropy loss do not improve the separation. On the other hand, the method that gives a margin to the angle between the feature vectors and the weight vectors of the last fully connected layer corresponding to each feature can improve the separation. Therefore, we propose a loss function that can improve the separation of the important class by setting the margin only for the important class, called Class-sensitive Additive Angular Margin Loss (CAMRI Loss). CAMRI loss is expected to reduce the variance of angles between features and weights of the important class relative to other classes due to the margin around the important class in the feature space by adding a penalty to the angle. In addition, concentrating the penalty only on the important classes hardly sacrifices the separation of the other classes. Experiments on CIFAR-10, GTSRB, and AwA2 showed that the proposed method could improve up to 9% recall improvement on cross-entropy loss without sacrificing accuracy.Comment: 2022 International Joint Conference on Neural Networks (IJCNN 2022

Global Linear Convergence of Evolution Strategies on More Than Smooth Strongly Convex Functions

International audienceEvolution strategies (ESs) are zero-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zero-order optimizers for difficult problems. Albeit ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zero-order and also first order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES, namely the (1 + 1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions

Global Linear Convergence of Evolution Strategies on More Than Smooth Strongly Convex Functions

Evolution strategies (ESs) are zero-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zero-order optimizers for difficult problems. Albeit ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zero-order and also first order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES, namely the (1 + 1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions

Study on environment conscious technologies in a super tall building: Evaluation of PV performance considering aerological climate

In recent years, buildings have tended to be taller, and their energy potential is expected be used effectively . Photovoltaics is considered one of technologies affected by air temperature, outside air velocity, and solar radiation from the aerological climate of supertall buildings with a height of 390 m. The energy potential of the “height” of photovoltaic power generation systems is affected by two factors: aerological climate and shadows cast by surrounding buildings. Taking these effects into account, the predicted annual power generation amount was calculated. At 390 m above ground, it was confirmed that the power generation amount was greater than that on the ground, when considering the effectiveness of photovoltaic systems. Then, we calculated the predicted annual power generation amount on each wall and roof surface of a tall building with a height of 390 m above the ground. By evaluating the energy-saving effect of adopting photovoltaic systems, we evaluated the photovoltaic system using the wall surface from the viewpoint of the primary energy reduction and primary energy consumption of the building

Development of HVAC Diffuser Unit for Task and Ambient Air Conditioning Allowing User to Control Built-in Fan — Evaluation of Air Supply Mode by Subjective Experiment and Field Measurement in Office

HVAC diffusers have been developed that have dual functions for task and ambient air conditioning. In this study, we evaluated comfort according to air supply mode, strong or fluctuation mode, through a subjective experiment. We found that the fluctuation mode maintained greater comfort for longer compared with the strong mode under continuous airflow exposure. Therefore, the fluctuation mode is considered suitable for long-duration use. Moreover, field measurements in an actual office showed that the fluctuation mode was superior in terms of both comfort and energy saving compared with conventional air conditioning