Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.Comment: 12 pages, 9 figure

BiometricBlender: Ultra-high dimensional, multi-class synthetic data generator to imitate biometric feature space

The lack of freely available (real-life or synthetic) high or ultra-high dimensional, multi-class datasets may hamper the rapidly growing research on feature screening, especially in the field of biometrics, where the usage of such datasets is common. This paper reports a Python package called BiometricBlender, which is an ultra-high dimensional, multi-class synthetic data generator to benchmark a wide range of feature screening methods. During the data generation process, the overall usefulness and the intercorrelations of blended features can be controlled by the user, thus the synthetic feature space is able to imitate the key properties of a real biometric dataset

Stimulus complexity shapes response correlations in primary visual cortex

Spike count correlations (SCCs) are ubiquitous in sensory cortices, are characterized by rich structure, and arise from structured internal dynamics. However, most theories of visual perception treat contributions of neurons to the representation of stimuli independently and focus on mean responses. Here, we argue that, in a functional model of visual perception, featuring probabilistic inference over a hierarchy of features, inferences about high-level features modulate inferences about low-level features ultimately introducing structured internal dynamics and patterns in SCCs. Specifically, high-level inferences for complex stimuli establish the local context in which neurons in the primary visual cortex (V1) interpret stimuli. Since the local context differentially affects multiple neurons, this conjecture predicts specific modulations in the fine structure of SCCs as stimulus identity and, more importantly, stimulus complexity varies. We designed experiments with natural and synthetic stimuli to measure the fine structure of SCCs in V1 of awake behaving macaques and assessed their dependence on stimulus identity and stimulus statistics. We show that the fine structure of SCCs is specific to the identity of natural stimuli and changes in SCCs are independent of changes in response mean. Critically, we demonstrate that stimulus specificity of SCCs in V1 can be directly manipulated by altering the amount of high-order structure in synthetic stimuli. Finally, we show that simple phenomenological models of V1 activity cannot account for the observed SCC patterns and conclude that the stimulus dependence of SCCs is a natural consequence of structured internal dynamics in a hierarchical probabilistic model of natural images

The contribution of response correlations to the neural code of V1

Contribution of joint statistics of neuron populations to stimulus encoding can distinguish theories of neural computation. Specifically, probabilistic inference in a hierarchical model of perception predicts the emergence of content-specific modulations in the fine structure of spike count correlations. By recording spiking activity from the V1 of behaving macaques viewing naturalistic and synthetic stimuli we demonstrate that compositional objects elicit correlational structures that are more specific to the identity of the stimulus than stimuli without structured content. Further, we demonstrate that decoding schemes exploiting stimulus-specific pairwise response statistics outperform those relying on marginal statistics, thus showing that joint statistics carry information about the stimulus independently from marginal statistics. To rule out possible simpler explanations of the observed patterns in the correlation structure, we introduce an array of controls. We develop Contrastive Rate Matching to control for firing rate-related changes in correlation magnitudes. Further, we analyze phenomenological models of noise correlations, the raster marginal model and a family of models featuring collective additive and/or multiplicative noise sources. Our results show that stimulus-dependence of noise correlations at the level of V1 reflect high-order structure in the stimulus, is independent of changes in firing rates and cannot be explained by phenomenological accounts