A large covariance matrix estimator under intermediate spikiness regimes

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus $l_1$ norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such un-shrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when $n$ is at least $O(p^{\frac{3}{2}\delta})$, provided that the maximum number of non-zeros per row in the sparse component is $O(p^{\delta})$ with $\delta \leq \frac{1}{2}$. Consistent recovery is ensured if the latent eigenvalues scale to $p^{\alpha}$, $\alpha \in[0,1]$, while rank consistency is ensured if $\delta \leq \alpha$. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data

Changing ideas about others' intentions: updating prior expectations tunes activity in the human motor system

Predicting intentions from observing another agent’s behaviours is often thought to depend on motor resonance – i.e., the motor system’s response to a perceived movement by the activation of its stored motor counterpart, but observers might also rely on prior expectations, especially when actions take place in perceptually uncertain situations. Here we assessed motor resonance during an action prediction task using transcranial magnetic stimulation to probe corticospinal excitability (CSE) and report that experimentally-induced updates in observers’ prior expectations modulate CSE when predictions are made under situations of perceptual uncertainty. We show that prior expectations are updated on the basis of both biomechanical and probabilistic prior information and that the magnitude of the CSE modulation observed across participants is explained by the magnitude of change in their prior expectations. These findings provide the first evidence that when observers predict others’ intentions, motor resonance mechanisms adapt to changes in their prior expectations. We propose that this adaptive adjustment might reflect a regulatory control mechanism that shares some similarities with that observed during action selection. Such a mechanism could help arbitrate the competition between biomechanical and probabilistic prior information when appropriate for prediction

The Rubber Hand Illusion: Two's a company, but three's a crowd

On the one hand, it is often assumed that the Rubber Hand Illusion (RHI) is constrained by a structural body model so that one cannot implement supernumerary limbs. On the other hand, several recent studies reported illusory duplication of the right hand in subjects exposed to two adjacent rubber hands. The present study tested whether spatial constraints may affect the possibility of inducing the sense of ownership to two rubber hands located side by side to the left of the subject's hand. We found that only the closest rubber hand appeared both objectively (proprioceptive drift) and subjectively (ownership rating) embodied. Crucially, synchronous touch of a second, but farther, rubber hand disrupted the objective measure of the RHI, but not the subjective one. We concluded that, in order to elicit a genuine RHI for multiple rubber hands, the two rubber hands must be at the same distance from the subject's hand/body

The plasticity of near space: evidence for contraction

The distinction between near space and the space farther away has been well established, as has the relation of this distinction to arm length. Recent studies provide evidence for the plasticity of near space, showing that it is possible to expand its extent ("size") through tool-use. In the present study, we examine the converse effect, whether contraction of near space results from increasing the effort involved on a line bisection task. Adult participants bisected lines at different distances, while, in some cases, wearing weights. In Experiment 1, the arms, specifically, were weighted (wrist weights), and in Experiment 2, more general body weights were used (heavy backpack). As in previous studies, unencumbered participants showed leftward bias when bisecting lines at the closest distances and a rightward shift in bias with increasingly farther distances. With wrist weights, but not a heavy backpack, participants showed more rightward bias at the closest distances, and a more gradual rightward shift with increasing distance, as if the nearest locations were represented as being farther away. These results suggest that increased effort, when specifically related to the arm, can serve to reduce the size of near space, providing support for the generally symmetrical plasticity of near space representations

Approaching stimuli bias attention in numerical space

Increasing evidence suggests that common mechanisms underlie the direction of attention in physical space and numerical space, along the mental number line. The small leftward bias (pseudoneglect) found on paper-and-pencil line bisection is also observed when participants ‘bisect’ number pairs, estimating (without calculating) the number midway between two others. Here we investigated the effect of stimulus motion on attention in numerical space. A two-frame apparent motion paradigm manipulating stimulus size was used to produce the impression that pairs of numbers were approaching (size increase from first to second frame), receding (size decrease), or not moving (no size change). The magnitude of pseudoneglect increased for approaching numbers, even when the final stimulus size was held constant. This result is consistent with previous findings that pseudoneglect in numerical space (as in physical space) increases as stimuli are brought closer to the participant. It also suggests that the perception of stimulus motion modulates attention over the mental number line and provides further support for a connection between the neural representations of physical space and number

Visual enhancement of touch and the bodily self

We experience our own body through both touch and vision. We further see that others’ bodies are similar to our own body, but we have no direct experience of touch on others’ bodies. Therefore, relations between vision and touch are important for the sense of self and for mental representation of one’s own body. For example, seeing the hand improves tactile acuity on the hand, compared to seeing a non-hand object. While several studies have demonstrated this visual enhancement of touch (VET) effect, its relation to the ‘bodily self’, or mental representation of one’s own body remains unclear. We examined whether VET is an effect of seeing a hand, or of seeing my hand, using the rubber hand illusion. In this illusion, a prosthetic hand which is brushed synchronously—but not asynchronously—with one’s own hand is felt to actually be one’s hand. Thus, we manipulated whether or not participants felt like they were looking directly at their hand, while holding the actual stimulus they viewed constant. Tactile acuity was measured by having participants judge the orientation of square-wave gratings. Two characteristic effects of VET were observed: (1) cross-modal enhancement from seeing the hand was inversely related to overall tactile acuity, and (2) participants near sensory threshold showed significant improvement following synchronous stroking, compared to asynchronous stroking or no stroking at all. These results demonstrate a clear functional relation between the bodily self and basic tactile perception

What is embodiment? a psychometric approach

What is it like to have a body? The present study takes a psychometric approach to this question. We collected structured introspective reports of the rubber hand illusion, to systematically investigate the structure of bodily self-consciousness. Participants observed a rubber hand that was stroked either synchronously or asynchronously with their own hand and then made proprioceptive judgments of the location of their own hand and used Likert scales to rate their agreement or disagreement with 27 statements relating to their subjective experience of the illusion. Principal components analysis of this data revealed four major components of the experience across conditions, which we interpret as: embodiment of rubber hand, loss of own hand, movement, and affect. In the asynchronous condition, an additional fifth component, deafference, was found. Secondary analysis of the embodiment of runner hand component revealed three subcomponents in both conditions: ownership, location, and agency. The ownership and location components were independent significant predictors of proprioceptive biases induced by the illusion. These results suggest that psychometric tools may provide a rich method for studying the structure of conscious experience, and point the way towards an empirically rigorous phenomenology