Linear Additive Markov Process (LAMP) 
We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP may be influenced by states visited in the distant history of the process, but unlike higher-order Markov processes, LAMP retains an efficient parametrization. LAMP also allows the specific dependence on history to be learned efficiently from data. We characterize some theoretical properties of LAMP, including its steady-state and mixing time. We then give an algorithm based on alternating minimization to learn LAMP models from data. Finally, we perform a series of real-world experiments to show that LAMP is more powerful than first-order Markov processes, and even holds its own against deep sequential models (LSTMs) with a negligible increase in parameter complexity. …
Short-Term Cognitive Network
While the machine learning literature dedicated to fully automated reasoning algorithms is abundant, the number of methods enabling the inference process on the basis of previously defined knowledge structures is scanter. Fuzzy Cognitive Maps (FCMs) are neural networks that can be exploited towards this goal because of their flexibility to handle external knowledge. However, FCMs suffer from a number of issues that range from the limited prediction horizon to the absence of theoretically sound learning algorithms able to produce accurate predictions. In this paper, we propose a neural network system named Short-term Cognitive Networks that tackle some of these limitations. In our model weights are not constricted and may have a causal nature or not. As a second contribution, we present a nonsynaptic learning algorithm to improve the network performance without modifying the previously defined weights. Moreover, we derive a stop condition to prevent the learning algorithm from iterating without decreasing the simulation error. …
PRObabilistic Parametric rEgression Loss (PROPEL)
Recently, Convolutional Neural Networks (CNNs) have dominated the field of computer vision. Their widespread success has been attributed to their representation learning capabilities. For classification tasks, CNNs have widely employed probabilistic output and have shown the significance of providing additional confidence for predictions. However, such probabilistic methodologies are not widely applicable for addressing regression problems using CNNs, as regression involves learning unconstrained continuous and, in many cases, multi-variate target variables. We propose a PRObabilistic Parametric rEgression Loss (PROPEL) that enables probabilistic regression using CNNs. PROPEL is fully differentiable and, hence, can be easily incorporated for end-to-end training of existing regressive CNN architectures. The proposed method is flexible as it learns complex unconstrained probabilities while being generalizable to higher dimensional multi-variate regression problems. We utilize a PROPEL-based CNN to address the problem of learning hand and head orientation from uncalibrated color images. Comprehensive experimental validation and comparisons with existing CNN regression loss functions are provided. Our experimental results indicate that PROPEL significantly improves the performance of a CNN, while reducing model parameters by 10x as compared to the existing state-of-the-art. …
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