The learning process in Boltzmann machines is computationally very expensive. The computational complexity of the exact algorithm is exponential in the number of neurons. We present a new approximate learning algorithm for Boltzmann machines, based on mean-field theory and the linear response theorem. The computational complexity of the algorithm is cubic in the number of neurons.In the absence of hidden units, we show how the weights can be directly computed from the fixed-point equation of the learning rules. Thus, in this case we do not need to use a gradient descent procedure for the learning process. We show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role. Finally, we apply the method to a pattern completion task and show good performance for networks up to 100 neurons.
We designed a novel assisted closed-loop optimization protocol to improve the efficiency of brain computer interfaces (BCI) based on steady state visually evoked potentials (SSVEP). In traditional paradigms, the control over the BCI-performance completely depends on the subjects’ ability to learn from the given feedback cues. By contrast, in the proposed protocol both the subject and the machine share information and control over the BCI goal. Generally, the innovative assistance consists in the delivery of online information together with the online adaptation of BCI stimuli properties. In our case, this adaptive optimization process is realized by (i) a closed-loop search for the best set of SSVEP flicker frequencies and (ii) feedback of actual SSVEP magnitudes to both the subject and the machine. These closed-loop interactions between subject and machine are evaluated in real-time by continuous measurement of their efficiencies, which are used as online criteria to adapt the BCI control parameters. The proposed protocol aims to compensate for variability in possibly unknown subjects’ state and trait dimensions. In a study with N = 18 subjects, we found significant evidence that our protocol outperformed classic SSVEP-BCI control paradigms. Evidence is presented that it takes indeed into account interindividual variabilities: e.g. under the new protocol, baseline resting state EEG measures predict subjects’ BCI performances. This paper illustrates the promising potential of assisted closed-loop protocols in BCI systems. Probably their applicability might be expanded to innovative uses, e.g. as possible new diagnostic/therapeutic tools for clinical contexts and as new paradigms for basic research.
The emergence of small handheld devices such as tablets and smartphones, often with touch sensitive surfaces as their only input modality, has spurred a growing interest in the subject of gestures for human–computer interaction (HCI). It has been proven before that eye movements can be consciously controlled by humans to the extent of performing sequences of predefined movement patterns, or “gaze gestures” that can be used for HCI purposes in desktop computers. Gaze gestures can be tracked noninvasively using a video-based eye-tracking system. We propose here that gaze gestures can also be an effective input paradigm to interact with handheld electronic devices. We show through a pilot user study how gaze gestures can be used to interact with a smartphone, how they are easily assimilated by potential users, and how the Needleman-Wunsch algorithm can effectively discriminate intentional gaze gestures from otherwise typical gaze activity performed during standard interaction with a small smartphone screen. Hence, reliable gaze–smartphone interaction is possible with accuracy rates, depending on the modality of gaze gestures being used (with or without dwell), higher than 80 to 90%, negligible false positive rates, and completion speeds lower than 1 to 1.5 s per gesture. These encouraging results and the low-cost eye-tracking equipment used suggest the possibilities of this new HCI modality for the field of interaction with small-screen handheld devices.