Shahram Dehdashti

Dimitris Gkoumas, Qiuchi Li, Shahram Dehdashti et al.

Video sentiment analysis as a decision-making process is inherently complex, involving the fusion of decisions from multiple modalities and the so-caused cognitive biases. Inspired by recent advances in quantum cognition, we show that the sentiment judgment from one modality could be incompatible with the judgment from another, i.e., the order matters and they cannot be jointly measured to produce a final decision. Thus the cognitive process exhibits "quantum-like" biases that cannot be captured by classical probability theories. Accordingly, we propose a fundamentally new, quantum cognitively motivated fusion strategy for predicting sentiment judgments. In particular, we formulate utterances as quantum superposition states of positive and negative sentiment judgments, and uni-modal classifiers as mutually incompatible observables, on a complex-valued Hilbert space with positive-operator valued measures. Experiments on two benchmarking datasets illustrate that our model significantly outperforms various existing decision level and a range of state-of-the-art content-level fusion approaches. The results also show that the concept of incompatibility allows effective handling of all combination patterns, including those extreme cases that are wrongly predicted by all uni-modal classifiers.

Prayag Tiwari, Shahram Dehdashti, Abdul Karim Obeid et al.

In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered when data is mapped to a complex Hilbert state represented by coherent states, non-linear coherent states can be considered as natural generalisation of associated kernels. By considering the non-linear coherent states of a quantum oscillator with variable mass, we propose a kernel function based on generalized hypergeometric functions, as orthogonal polynomial functions. The suggested kernel is implemented with support vector machine on two well known datasets (make circles, and make moons) and outperforms the baselines, even in the presence of high noise. In addition, we study impact of geometrical properties of feature space, obtaining by non-linear coherent states, on the SVM classification task, by using considering the Fubini-Study metric of associated coherent states.

Shahram Dehdashti, Catarina Moreira, Abdul Karim Obeid et al.

This paper uses deformed coherent states, based on a deformed Weyl-Heisenberg algebra that unifies the well-known SU(2), Weyl-Heisenberg, and SU(1,1) groups, through a common parameter. We show that deformed coherent states provide the theoretical foundation of a meta-kernel function, that is a kernel which in turn defines kernel functions. Kernel functions drive developments in the field of machine learning and the meta-kernel function presented in this paper opens new theoretical avenues for the definition and exploration of kernel functions. The meta-kernel function applies associated revolution surfaces as feature spaces identified with non-linear coherent states. An empirical investigation compares the deformed SU(2) and SU(1,1) kernels derived from the meta-kernel which shows performance similar to the Radial Basis kernel, and offers new insights (based on the deformed Weyl-Heisenberg algebra).

Sagar Uprety, Prayag Tiwari, Shahram Dehdashti et al.

A large number of studies in cognitive science have revealed that probabilistic outcomes of certain human decisions do not agree with the axioms of classical probability theory. The field of Quantum Cognition provides an alternative probabilistic model to explain such paradoxical findings. It posits that cognitive systems have an underlying quantum-like structure, especially in decision-making under uncertainty. In this paper, we hypothesise that relevance judgement, being a multidimensional, cognitive concept, can be used to probe the quantum-like structure for modelling users' cognitive states in information seeking. Extending from an experiment protocol inspired by the Stern-Gerlach experiment in Quantum Physics, we design a crowd-sourced user study to show violation of the Kolmogorovian probability axioms as a proof of the quantum-like structure, and provide a comparison between a quantum probabilistic model and a Bayesian model for predictions of relevance.

Sagar Uprety, Shahram Dehdashti, Lauren Fell et al.

Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these dimensions, where their interaction and fusion leads to the final inference of relevance. We study the interaction between the relevance dimensions using the mathematical framework of Quantum Theory. It is considered a generalised framework to model decision making under uncertainty, involving multiple perspectives and influenced by context. Specifically, we conduct a user study by constructing the cognitive analogue of a famous experiment in Quantum Physics. The data is used to construct a complex-valued vector space model of the user's cognitive state, which is used to explain incompatibility and interference between relevance dimensions. The implications of our findings to inform the design of Information Retrieval systems are also discussed.

Catarina Moreira, Lauren Fell, Shahram Dehdashti et al.

We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This framework can accommodate and predict several cognitive biases reported in Lieder & Griffiths without heavy reliance on heuristics nor on assumptions of the computational resources of the mind.