Discovering Correlation Indices for Link Prediction Using Differential Evolution

Binary correlation indices are crucial for forecasting and modelling tasks in different areas of scientific research. The setting of sound binary correlations and similarity measures is a long and mostly empirical interactive process, in which researchers start from experimental correlations in one domain, which usually prove to be effective in other similar fields, and then progressively evaluate and modify those correlations to adapt their predictive power to the specific characteristics of the domain under examination. In the research of prediction of links on complex networks, it has been found that no single correlation index can always obtain excellent results, even in similar domains. The research of domain-specific correlation indices or the adaptation of known ones is therefore a problem of critical concern. This paper presents a solution to the problem of setting new binary correlation indices that achieve efficient performances on specific network domains. The proposed solution is based on Differential Evolution, evolving the coefficient vectors of meta-correlations, structures that describe classes of binary similarity indices and subsume the most known correlation indices for link prediction. Experiments show that the proposed evolutionary approach always results in improved performances, and in some cases significantly enhanced, compared to the best correlation indices available in the link prediction literature, effectively exploring the correlation space and exploiting its self-adaptability to the given domain to improve over generations.

Full Function Sampling of Uncertain Correlations

Empirically-based correlations are commonly used in modeling and simulation but rarely have rigorous uncertainty quantification that captures the nature of the underlying data. In many applications, a mathematical description for a parameter response to some input stimulus is often either unknown, unable to be measured, or both. Likewise, the data used to observe a parameter response is often noisy, and correlations are derived to approximate the bulk response. Practitioners frequently treat the chosen correlation — sometimes referred to as the “surrogate” or “reduced-order” model of the response — as a constant mathematical description of the relationship between input and output. This assumption, as with any model, is incorrect to some degree, and the uncertainty in the correlation can potentially have significant impacts on system responses. Thus, proper treatment of correlation uncertainty is necessary. In this paper, a method is proposed for high-level abstract sampling of uncertain data correlations. Whereas uncertainty characterization is often assigned to scalar values for direct sampling, functional uncertainty is not always straightforward. A systematic approach for sampling univariable uncertain correlations was developed to perform more rigorous uncertainty analyses and more reliably sample the correlation space. This procedure implements pseudo-random sampling of a correlation with a bounded input range to maintain the correlation form, to respect variable uncertainty across the range, and to ensure function continuity with respect to the input variable.

Noise in one-dimensional measurement-based quantum computing

Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum circuit model, whereby the computation proceeds via measurements on an entangled resource state. Noise processes are a major experimental challenge to the construction of a quantum computer. Here, we investigate how noise processes affecting physical states affect the performed computation by considering MBQC on a one-dimensional cluster state. This allows us to break down the computation in a sequence of building blocks and map physical errors to logical errors. Next, we extend the Matrix Product State construction to mixed states (which is known as Matrix Product Operators) and once again map the effect of physical noise to logical noise acting within the correlation space. This approach allows us to consider more general errors than the conventional Pauli errors, and could be used in order to simulate noisy quantum computation.