Inference on copula-based correlation structures

We propose an extension of the approach provided by Kluppelberg and Kuhn (2009) for inference on second-order structure moments. As in Kluppelberg and Kuhn (2009) we adopt a copula-based approach instead of assuming normal distribution for the variables, thus relaxing the equality in distribution assumption. A new copula-based estimator for structure moments is investigated. The methodology provided by Kluppelberg and Kuhn (2009) is also extended considering the copulas associated with the family of Eyraud-Farlie-Gumbel-Morgenstern distribution functions (Kotz, Balakrishnan, and Johnson, 2000, Equation 44.73). Finally, a comprehensive simulation study and an application to real financial data are performed in order to compare the different approaches.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Hierarchical active inference for cognitive architectures

This thesis explores the methods based on the free energy principle and active inference for modelling cognition. Active inference is an emerging framework for designing intelligent agents where psychological processes are cast in terms of Bayesian inference. Here, I appeal to it to test the design of a set of cognitive architectures, via simulation. These architectures are defined in terms of generative models where an agent executes a task under the assumption that all cognitive processes aspire to the same objective: the minimization of variational free energy. Chapter 1 introduces the free energy principle and its assumptions about self-organizing systems. Chapter 2 describes how from the mechanics of self-organization can emerge a minimal form of cognition able to achieve autopoiesis. In chapter 3 I present the method of how I formalize generative models for action and perception. The architectures proposed allow providing a more biologically plausible account of more complex cognitive processing that entails deep temporal features. I then present three simulation studies that aim to show different aspects of cognition, their associated behavior and the underlying neural dynamics. In chapter 4, the first study proposes an architecture that represents the visuomotor system for the encoding of actions during action observation, understanding and imitation. In chapter 5, the generative model is extended and is lesioned to simulate brain damage and neuropsychological patterns observed in apraxic patients. In chapter 6, the third study proposes an architecture for cognitive control and the modulation of attention for action selection. At last, I argue how active inference can provide a formal account of information processing in the brain and how the adaptive capabilities of the simulated agents are a mere consequence of the architecture of the generative models. Cognitive processing, then, becomes an emergent property of the minimization of variational free energy.

Considerations on indirect adhesive restorations at the material and tooth interfaces

Objective: Lithium-silicate (LiSi) ceramic is nowadays widely used in dentistry. However, for the longevity of LiSi indirect restorations, it is important to pretreat the material and the dental substrate adequately. However, is not certain how the simplification of the manufacturing and conditioning procedures influences the bonding performances of LiSi ceramic restorations. Accordingly, the aims of this thesis were to investigate the effect of: 1) different LiSi ceramic surface decontamination procedures on the shear bond strength (SBS) to resin composite; 2) different types of lithium-disilicate (LiDi) (pressed vs CAD-CAM) on SBS to resin composite; 3) an experimental metal salt-based zirconium oxynitrate etchant [ZrO(NO3)2] on bonding performances to dentin. Materials and Methods: SBS test was used to investigate the influence of different cleaning protocols applied, or different processing techniques (CAD or PRESS) on the bond strength to composite resin. The third study tackled the interface between restorative materials and dentin, and investigated the microtensile bond strength test (µTBS), nanoleakage expression analysis (NL), gelatin zymography and in situ zymography of dentin conditioned with an experimental metal salt-based zirconium oxynitrate etchant [ZrO(NO3)2]. Results: MEP showed comparable bond strength to the double HP etching and higher compared to other groups. BS of press LiSi to composite was higher than that of CAD/CAM LiSi. ZON pretreatment increased bond strength to dentin when used with a universal adhesive, and inhibited dentinal endogenous enzymes. Conclusions: While simplification of the LiSi conditioning and cleaning procedures seems to yield bond strength comparable to the traditional procedures, it could be recommended in the clinical practice. However, pressed LiSi still seems to perform better in terms of bond strength compared to the CAD/CAM LiSi. Further, the novel ZON etchant seems to perform better compared to the traditional phosphoric dentin etching.