Random Search Plus: A more effective random search for machine learning hyperparameters optimization

Machine learning hyperparameter optimization has always been the key to improve model performance. There are many methods of hyperparameter optimization. The popular methods include grid search, random search, manual search, Bayesian optimization, population-based optimization, etc. Random search occupies less computations than the grid search, but at the same time there is a penalty for accuracy. However, this paper proposes a more effective random search method based on the traditional random search and hyperparameter space separation. This method is named random search plus. This thesis empirically proves that random search plus is more effective than random search. There are some case studies to do a comparison between them, which consists of four different machine learning algorithms including K-NN, K-means, Neural Networks and Support Vector Machine as optimization objects with three different size datasets including Iris flower, Pima Indians diabetes and MNIST handwritten dataset. Compared to traditional random search, random search plus can find a better hyperparameters or do an equivalent optimization as random search but with less time at most cases. With a certain hyperparameter space separation strategy, it can only need 10% time of random search to do an equivalent optimization or it can increase both the accuracy of supervised leanings and the silhouette coefficient of a supervised learning by 5%-30% in a same runtime as random search. The distribution of the best hyperparameters searched by the two methods in the hyperparameters space shows that random search plus is more global than random search. The thesis also discusses about some future works like the feasibility of using genetic algorithm to improve the local optimization ability of random search plus, space division of non-integer hyperparameters, etc

Local Search For SMT On Linear and Multilinear Real Arithmetic

Satisfiability Modulo Theories (SMT) has significant application in various domains. In this paper, we focus on quantifier-free Satisfiablity Modulo Real Arithmetic, referred to as SMT(RA), including both linear and non-linear real arithmetic theories. As for non-linear real arithmetic theory, we focus on one of its important fragments where the atomic constraints are multi-linear. We propose the first local search algorithm for SMT(RA), called LocalSMT(RA), based on two novel ideas. First, an interval-based operator is proposed to cooperate with the traditional local search operator by considering the interval information. Moreover, we propose a tie-breaking mechanism to further evaluate the operations when the operations are indistinguishable according to the score function. Experiments are conducted to evaluate LocalSMT(RA) on benchmarks from SMT-LIB. The results show that LocalSMT(RA) is competitive with the state-of-the-art SMT solvers, and performs particularly well on multi-linear instances

An Efficient Data Analysis Method for Big Data using Multiple-Model Linear Regression

This paper introduces a new data analysis method for big data using a newly defined regression model named multiple model linear regression(MMLR), which separates input datasets into subsets and construct local linear regression models of them. The proposed data analysis method is shown to be more efficient and flexible than other regression based methods. This paper also proposes an approximate algorithm to construct MMLR models based on $(\epsilon,\delta)$-estimator, and gives mathematical proofs of the correctness and efficiency of MMLR algorithm, of which the time complexity is linear with respect to the size of input datasets. This paper also empirically implements the method on both synthetic and real-world datasets, the algorithm shows to have comparable performance to existing regression methods in many cases, while it takes almost the shortest time to provide a high prediction accuracy

Spectral flow, twisted modules and MLDE of quasi-lisse vertex algebras

We calculate the fusion rules among $\mathbb{Z}_2$-twisted modules $L_{\mathfrak{sl}_2}(\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples include affine VOAs of type $A_1^{(1)}$ at boundary admissible level, admissible level $k=-1/2$, $A^{(1)}_{2}$ at boundary admissible level $k=-3/2$, and $\mathrm{BP}^{k}$-algebra with special value $k=-9/4$. We also derive characters of some non-vacuum modules for affine VOA of type $D_4$ at non-admissible level $-2$ from spectral flow automorphism

Context-Dependent Diffusion Network for Visual Relationship Detection

Visual relationship detection can bridge the gap between computer vision and natural language for scene understanding of images. Different from pure object recognition tasks, the relation triplets of subject-predicate-object lie on an extreme diversity space, such as \textit{person-behind-person} and \textit{car-behind-building}, while suffering from the problem of combinatorial explosion. In this paper, we propose a context-dependent diffusion network (CDDN) framework to deal with visual relationship detection. To capture the interactions of different object instances, two types of graphs, word semantic graph and visual scene graph, are constructed to encode global context interdependency. The semantic graph is built through language priors to model semantic correlations across objects, whilst the visual scene graph defines the connections of scene objects so as to utilize the surrounding scene information. For the graph-structured data, we design a diffusion network to adaptively aggregate information from contexts, which can effectively learn latent representations of visual relationships and well cater to visual relationship detection in view of its isomorphic invariance to graphs. Experiments on two widely-used datasets demonstrate that our proposed method is more effective and achieves the state-of-the-art performance.Comment: 8 pages, 3 figures, 2018 ACM Multimedia Conference (MM'18

SocioHub: An Interactive Tool for Cross-Platform Social Media Data Collection

Social media is inherently about connecting and interacting with others. Different social media platforms have unique characteristics and user bases. Moreover, people use different platforms for various social and entertainment purposes. Analyzing cross-platform user behavior can provide insights into the preferences and expectations of users on each platform. By understanding how users behave and interact across platforms, we can build an understanding of content consumption patterns, enhance communication and social interactions, and tailor platform-specific strategies. We can further gather insights into how users navigate and engage with their platforms on different devices. In this work, we develop a tool SocioHub, which enables users to gather data on multiple social media platforms in one place. This tool can help researchers gain insights into different data attributes for users across social media platforms such as Twitter, Instagram, and Mastodon. Keywords: Social Media Platforms, Twitter, Instagram, Mastodon.Comment: 5 pages, 2 figure

Optimal Monotone Mean-Variance Problem in a Catastrophe Insurance Model

This paper explores an optimal investment and reinsurance problem involving both ordinary and catastrophe insurance businesses. The catastrophic events are modeled as following a compound Poisson process, impacting the ordinary insurance business. The claim intensity for the ordinary insurance business is described using a Cox process with a shot-noise intensity, the jump of which is proportional to the size of the catastrophe event. This intensity increases when a catastrophe occurs and then decays over time. The insurer's objective is to maximize their terminal wealth under the Monotone Mean-Variance (MMV) criterion. In contrast to the classical Mean-Variance (MV) criterion, the MMV criterion is monotonic across its entire domain, aligning better with fundamental economic principles. We first formulate the original MMV optimization problem as an auxiliary zero-sum game. Through solving the Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation, explicit forms of the value function and optimal strategies are obtained. Additionally, we provides the efficient frontier within the MMV criterion. Several numerical examples are presented to demonstrate the practical implications of the results