Applying Deep Bidirectional LSTM and Mixture Density Network for Basketball Trajectory Prediction

Data analytics helps basketball teams to create tactics. However, manual data collection and analytics are costly and ineffective. Therefore, we applied a deep bidirectional long short-term memory (BLSTM) and mixture density network (MDN) approach. This model is not only capable of predicting a basketball trajectory based on real data, but it also can generate new trajectory samples. It is an excellent application to help coaches and players decide when and where to shoot. Its structure is particularly suitable for dealing with time series problems. BLSTM receives forward and backward information at the same time, while stacking multiple BLSTMs further increases the learning ability of the model. Combined with BLSTMs, MDN is used to generate a multi-modal distribution of outputs. Thus, the proposed model can, in principle, represent arbitrary conditional probability distributions of output variables. We tested our model with two experiments on three-pointer datasets from NBA SportVu data. In the hit-or-miss classification experiment, the proposed model outperformed other models in terms of the convergence speed and accuracy. In the trajectory generation experiment, eight model-generated trajectories at a given time closely matched real trajectories

FRMDN: Flow-based Recurrent Mixture Density Network

Recurrent Mixture Density Networks (RMDNs) are consisted of two main parts: a Recurrent Neural Network (RNN) and a Gaussian Mixture Model (GMM), in which a kind of RNN (almost LSTM) is used to find the parameters of a GMM in every time step. While available RMDNs have been faced with different difficulties. The most important of them is high$-$dimensional problems. Since estimating the covariance matrix for the high$-$dimensional problems is more difficult, due to existing correlation between dimensions and satisfying the positive definition condition. Consequently, the available methods have usually used RMDN with a diagonal covariance matrix for high$-$dimensional problems by supposing independence among dimensions. Hence, in this paper with inspiring a common approach in the literature of GMM, we consider a tied configuration for each precision matrix (inverse of the covariance matrix) in RMDN as (\(\Sigma _k^{ - 1} = U{D_k}U\)) to enrich GMM rather than considering a diagonal form for it. But due to simplicity, we assume \(U\) be an Identity matrix and \(D_k\) is a specific diagonal matrix for \(k^{th}\) component. Until now, we only have a diagonal matrix and it does not differ with available diagonal RMDNs. Besides, Flow$-$based neural networks are a new group of generative models that are able to transform a distribution to a simpler distribution and vice versa, through a sequence of invertible functions. Therefore, we applied a diagonal GMM on transformed observations. At every time step, the next observation, \({y_{t + 1}}\), has been passed through a flow$-$based neural network to obtain a much simpler distribution. Experimental results for a reinforcement learning problem verify the superiority of the proposed method to the base$-$line method in terms of Negative Log$-$Likelihood (NLL) for RMDN and the cumulative reward for a controller with fewer population size

Synaptic mechanisms of interference in working memory

Information from preceding trials of cognitive tasks can bias performance in the current trial, a phenomenon referred to as interference. Subjects performing visual working memory tasks exhibit interference in their trial-to-trial response correlations: the recalled target location in the current trial is biased in the direction of the target presented on the previous trial. We present modeling work that (a) develops a probabilistic inference model of this history-dependent bias, and (b) links our probabilistic model to computations of a recurrent network wherein short-term facilitation accounts for the dynamics of the observed bias. Network connectivity is reshaped dynamically during each trial, providing a mechanism for generating predictions from prior trial observations. Applying timescale separation methods, we can obtain a low-dimensional description of the trial-to-trial bias based on the history of target locations. The model has response statistics whose mean is centered at the true target location across many trials, typical of such visual working memory tasks. Furthermore, we demonstrate task protocols for which the plastic model performs better than a model with static connectivity: repetitively presented targets are better retained in working memory than targets drawn from uncorrelated sequences.Comment: 28 pages, 7 figure

Digging Deeper into Egocentric Gaze Prediction

This paper digs deeper into factors that influence egocentric gaze. Instead of training deep models for this purpose in a blind manner, we propose to inspect factors that contribute to gaze guidance during daily tasks. Bottom-up saliency and optical flow are assessed versus strong spatial prior baselines. Task-specific cues such as vanishing point, manipulation point, and hand regions are analyzed as representatives of top-down information. We also look into the contribution of these factors by investigating a simple recurrent neural model for ego-centric gaze prediction. First, deep features are extracted for all input video frames. Then, a gated recurrent unit is employed to integrate information over time and to predict the next fixation. We also propose an integrated model that combines the recurrent model with several top-down and bottom-up cues. Extensive experiments over multiple datasets reveal that (1) spatial biases are strong in egocentric videos, (2) bottom-up saliency models perform poorly in predicting gaze and underperform spatial biases, (3) deep features perform better compared to traditional features, (4) as opposed to hand regions, the manipulation point is a strong influential cue for gaze prediction, (5) combining the proposed recurrent model with bottom-up cues, vanishing points and, in particular, manipulation point results in the best gaze prediction accuracy over egocentric videos, (6) the knowledge transfer works best for cases where the tasks or sequences are similar, and (7) task and activity recognition can benefit from gaze prediction. Our findings suggest that (1) there should be more emphasis on hand-object interaction and (2) the egocentric vision community should consider larger datasets including diverse stimuli and more subjects.Comment: presented at WACV 201

Dynamical laser spike processing

Novel materials and devices in photonics have the potential to revolutionize optical information processing, beyond conventional binary-logic approaches. Laser systems offer a rich repertoire of useful dynamical behaviors, including the excitable dynamics also found in the time-resolved "spiking" of neurons. Spiking reconciles the expressiveness and efficiency of analog processing with the robustness and scalability of digital processing. We demonstrate that graphene-coupled laser systems offer a unified low-level spike optical processing paradigm that goes well beyond previously studied laser dynamics. We show that this platform can simultaneously exhibit logic-level restoration, cascadability and input-output isolation---fundamental challenges in optical information processing. We also implement low-level spike-processing tasks that are critical for higher level processing: temporal pattern detection and stable recurrent memory. We study these properties in the context of a fiber laser system, but the addition of graphene leads to a number of advantages which stem from its unique properties, including high absorption and fast carrier relaxation. These could lead to significant speed and efficiency improvements in unconventional laser processing devices, and ongoing research on graphene microfabrication promises compatibility with integrated laser platforms.Comment: 13 pages, 7 figure