Learning performance of regularized regression with multiscale kernels based on Markov observations

In the last few years, many known works in learning theory stepped over the classical assumption that samples are independent and identical distribution and investigated learning performance based on non-independent samples, as mixing sequences (e.g., [Formula: see text]-mixing, [Formula: see text]-mixing, [Formula: see text]-mixing etc.), they derived similar results with the investigation based on classical sample assumption. Negative association (NA) sequence is a kind of significant dependent random variables and plays an important role in non-independent sequences. It is widely applied to various subjects such as probability theory, statistics and stochastic processes. Therefore, it is essential to study the learning performance of learning process for dependent samples drawn from NA process. Obviously, samples in this learning process are not independent and identical distribution. The results in classical learning theory are not applied directly. In this paper, we study the consistency of least-square regularized regression with NA samples. We establish the error bound of least-square regularized regression for NA samples, and prove that the learning rate of least-square regularized regression for NA samples is [Formula: see text], which is tend to [Formula: see text] when [Formula: see text] arbitrarily close to 0, where [Formula: see text] denote the number of the samples. The simulation experiment of convergence rate on NA samples reveals that the least-square regularized regression algorithm for NA samples is consistent. This result generalizes the classical result of independent and identical distribution.

Download Full-text

Learning and Consolidation of Verbal Declarative Memory in Patients with Posttraumatic Stress Disorder

Zeitschrift für Psychologie / Journal of Psychology ◽

10.1027/0044-3409/a000020 ◽

2010 ◽

Vol 218 (2) ◽

pp. 135-140 ◽

Cited By ~ 1

Author(s):

Slawomira J. Diener ◽

Herta Flor ◽

Michèle Wessa

Keyword(s):

Posttraumatic Stress Disorder ◽

Posttraumatic Stress ◽

Verbal Memory ◽

Stress Disorder ◽

Declarative Memory ◽

Memory Performance ◽

Verbal Learning ◽

Depression Scale ◽

Learning Performance ◽

Ptsd Symptoms

Impairments in declarative memory have been reported in posttraumatic stress disorder (PTSD). Fragmentation of explicit trauma-related memory has been assumed to impede the formation of a coherent memorization of the traumatic event and the integration into autobiographic memory. Together with a strong non-declarative memory that connects trauma reminders with a fear response the impairment in declarative memory is thought to be involved in the maintenance of PTSD symptoms. Fourteen PTSD patients, 14 traumatized subjects without PTSD, and 13 non-traumatized healthy controls (HC) were tested with the California Verbal Learning Test (CVLT) to assess verbal declarative memory. PTSD symptoms were assessed with the Clinician Administered PTSD Scale and depression with the Center of Epidemiological Studies Depression Scale. Several indices of the CVLT pointed to an impairment in declarative memory performance in PTSD, but not in traumatized persons without PTSD or HC. No group differences were observed if recall of memory after a time delay was set in relation to initial learning performance. In the PTSD group verbal memory performance correlated significantly with hyperarousal symptoms, after concentration difficulties were accounted for. The present study confirmed previous reports of declarative verbal memory deficits in PTSD. Extending previous results, we propose that learning rather than memory consolidation is impaired in PTSD patients. Furthermore, arousal symptoms may interfere with successful memory formation in PTSD.

Download Full-text