Dynamical and Statistical Criticality in a Model of Neural Tissue

For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongly stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian' behavior: {\sl all} degrees of freedom achieve a close balance of excitation and inhibition and become "critical" in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex "breakout" dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense

Efficient Data Representation by Selecting Prototypes with Importance Weights

Prototypical examples that best summarizes and compactly represents an underlying complex data distribution communicate meaningful insights to humans in domains where simple explanations are hard to extract. In this paper we present algorithms with strong theoretical guarantees to mine these data sets and select prototypes a.k.a. representatives that optimally describes them. Our work notably generalizes the recent work by Kim et al. (2016) where in addition to selecting prototypes, we also associate non-negative weights which are indicative of their importance. This extension provides a single coherent framework under which both prototypes and criticisms (i.e. outliers) can be found. Furthermore, our framework works for any symmetric positive definite kernel thus addressing one of the key open questions laid out in Kim et al. (2016). By establishing that our objective function enjoys a key property of that of weak submodularity, we present a fast ProtoDash algorithm and also derive approximation guarantees for the same. We demonstrate the efficacy of our method on diverse domains such as retail, digit recognition (MNIST) and on publicly available 40 health questionnaires obtained from the Center for Disease Control (CDC) website maintained by the US Dept. of Health. We validate the results quantitatively as well as qualitatively based on expert feedback and recently published scientific studies on public health, thus showcasing the power of our technique in providing actionability (for retail), utility (for MNIST) and insight (on CDC datasets) which arguably are the hallmarks of an effective data mining method.Comment: Accepted for publication in International Conference on Data Mining (ICDM) 201

Context Attentive Bandits: Contextual Bandit with Restricted Context

We consider a novel formulation of the multi-armed bandit model, which we call the contextual bandit with restricted context, where only a limited number of features can be accessed by the learner at every iteration. This novel formulation is motivated by different online problems arising in clinical trials, recommender systems and attention modeling. Herein, we adapt the standard multi-armed bandit algorithm known as Thompson Sampling to take advantage of our restricted context setting, and propose two novel algorithms, called the Thompson Sampling with Restricted Context(TSRC) and the Windows Thompson Sampling with Restricted Context(WTSRC), for handling stationary and nonstationary environments, respectively. Our empirical results demonstrate advantages of the proposed approaches on several real-life datasetsComment: IJCAI 201

Noise-induced memory in extended excitable systems

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states. The exponents are robust and model-independent. We discuss novel implications of these results for the functioning of cortical neurons as well as for networks of neurons.Comment: 4 pages, latex + 5 eps figure

Computational Models of Adult Neurogenesis

Experimental results in recent years have shown that adult neurogenesis is a significant phenomenon in the mammalian brain. Little is known, however, about the functional role played by the generation and destruction of neurons in the context of and adult brain. Here we propose two models where new projection neurons are incorporated. We show that in both models, using incorporation and removal of neurons as a computational tool, it is possible to achieve a higher computational efficiency that in purely static, synapse-learning driven networks. We also discuss the implication for understanding the role of adult neurogenesis in specific brain areas.Comment: To appear Physica A, 7 page

Online Learning in Iterated Prisoner's Dilemma to Mimic Human Behavior

Prisoner's Dilemma mainly treat the choice to cooperate or defect as an atomic action. We propose to study online learning algorithm behavior in the Iterated Prisoner's Dilemma (IPD) game, where we explored the full spectrum of reinforcement learning agents: multi-armed bandits, contextual bandits and reinforcement learning. We have evaluate them based on a tournament of iterated prisoner's dilemma where multiple agents can compete in a sequential fashion. This allows us to analyze the dynamics of policies learned by multiple self-interested independent reward-driven agents, and also allows us study the capacity of these algorithms to fit the human behaviors. Results suggest that considering the current situation to make decision is the worst in this kind of social dilemma game. Multiples discoveries on online learning behaviors and clinical validations are stated.Comment: To the best of our knowledge, this is the first attempt to explore the full spectrum of reinforcement learning agents (multi-armed bandits, contextual bandits and reinforcement learning) in the sequential social dilemma. This mental variants section supersedes and extends our work arXiv:1706.02897 (MAB), arXiv:2005.04544 (CB) and arXiv:1906.11286 (RL) into the multi-agent settin

Predicting human decision making in psychological tasks with recurrent neural networks

Unlike traditional time series, the action sequences of human decision making usually involve many cognitive processes such as beliefs, desires, intentions and theory of mind, i.e. what others are thinking. This makes predicting human decision making challenging to be treated agnostically to the underlying psychological mechanisms. We propose to use a recurrent neural network architecture based on long short-term memory networks (LSTM) to predict the time series of the actions taken by the human subjects at each step of their decision making, the first application of such methods in this research domain. In this study, we collate the human data from 8 published literature of the Iterated Prisoner's Dilemma comprising 168,386 individual decisions and postprocess them into 8,257 behavioral trajectories of 9 actions each for both players. Similarly, we collate 617 trajectories of 95 actions from 10 different published studies of Iowa Gambling Task experiments with healthy human subjects. We train our prediction networks on the behavioral data from these published psychological experiments of human decision making, and demonstrate a clear advantage over the state-of-the-art methods in predicting human decision making trajectories in both single-agent scenarios such as the Iowa Gambling Task and multi-agent scenarios such as the Iterated Prisoner's Dilemma. In the prediction, we observe that the weights of the top performers tends to have a wider distribution, and a bigger bias in the LSTM networks, which suggests possible interpretations for the distribution of strategies adopted by each group

Topological Effects of Synaptic Time Dependent Plasticity

We show that the local Spike Timing-Dependent Plasticity (STDP) rule has the effect of regulating the trans-synaptic weights of loops of any length within a simulated network of neurons. We show that depending on STDP's polarity, functional loops are formed or eliminated in networks driven to normal spiking conditions by random, partially correlated inputs, where functional loops comprise weights that exceed a non-zero threshold. We further prove that STDP is a form of loop-regulating plasticity for the case of a linear network comprising random weights drawn from certain distributions. Thus a notable local synaptic learning rule makes a specific prediction about synapses in the brain in which standard STDP is present: that under normal spiking conditions, they should participate in predominantly feed-forward connections at all scales. Our model implies that any deviations from this prediction would require a substantial modification to the hypothesized role for standard STDP. Given its widespread occurrence in the brain, we predict that STDP could also regulate long range synaptic loops among individual neurons across all brain scales, up to, and including, the scale of global brain network topology.Comment: 26 pages, 5 figure