Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing literature defines this intrinsic dimension as the Minkowski dimension or the manifold dimension of the support of the underlying probability measures, which often results in sub-optimal rates and unrealistic assumptions. In this paper, we consider supervised deep learning when the response given the explanatory variable is distributed according to an exponential family with a $\beta$-H\"older smooth mean function. We consider an entropic notion of the intrinsic data-dimension and demonstrate that with $n$ independent and identically distributed samples, the test error scales as $\tilde{\mathcal{O}}\left(n^{-\frac{2\beta}{2\beta + \bar{d}_{2\beta}(\lambda)}}\right)$, where $\bar{d}_{2\beta}(\lambda)$ is the $2\beta$-entropic dimension of $\lambda$, the distribution of the explanatory variables. This improves on the best-known rates. Furthermore, under the assumption of an upper-bounded density of the explanatory variables, we characterize the rate of convergence as $\tilde{\mathcal{O}}\left( d^{\frac{2\lfloor\beta\rfloor(\beta + d)}{2\beta + d}}n^{-\frac{2\beta}{2\beta + d}}\right)$, establishing that the dependence on $d$ is not exponential but at most polynomial. We also demonstrate that when the explanatory variable has a lower bounded density, this rate in terms of the number of data samples, is nearly optimal for learning the dependence structure for exponential families.

Supervised Deep Learning is similar to concept learning in humans and animals, the difference being that the student in the former case is a computational network. Supervised deep learning frameworks are trained using well-labelled data. It teaches the learning algorithm to generalise from the training data and to implement in unseen situations. After completing the training process, the model is tested on a subset of the testing set to predict the output. Thus, datasets containing inputs and correct outputs become critical as they help the model learn faster. Regression and classification are two subfields of supervised machine learning.

Supervised Deep Learning is similar to concept learning in humans and animals, the difference being that the student in the former case is a computational network. Supervised deep learning frameworks are trained using well-labelled data. It teaches the learning algorithm to generalise from the training data and to implement in unseen situations. After completing the training process, the model is tested on a subset of the testing set to predict the output. Thus, datasets containing inputs and correct outputs become critical as they help the model learn faster. Regression and classification are two subfields of supervised machine learning.

Purpose Supervised deep learning in radiology suffers from notorious inherent limitations: 1) It requires large, hand-annotated data sets, 2) It is non-generalizable, and 3) It lacks explainability and intuition. We have recently proposed Reinforcement Learning to address all threes. However, we applied it to images with radiologist eye tracking points, which limits the state-action space. Here we generalize the Deep-Q Learning to a gridworld-based environment, so that only the images and image masks are required. Materials and Methods We trained a Deep Q network on 30 two-dimensional image slices from the BraTS brain tumor database. Each image contained one lesion. We then tested the trained Deep Q network on a separate set of 30 testing set images. For comparison, we also trained and tested a keypoint detection supervised deep learning network for the same set of training / testing images. Results Whereas the supervised approach quickly overfit the training data, and predicably performed poorly on the testing set (11\% accuracy), the Deep-Q learning approach showed progressive improved generalizability to the testing set over training time, reaching 70\% accuracy. Conclusion We have shown a proof-of-principle application of reinforcement learning to radiological images, here using 2D contrast-enhanced MRI brain images with the goal of localizing brain tumors. This represents a generalization of recent work to a gridworld setting, naturally suitable for analyzing medical images.

As a basis for modelling brain function, deep learning has in recent years been used to model systems in vision, audition, motor control, navigation, and cognitive control. In a new paper, DeepMind researchers call attention to another "fundamentally novel" development in AI research -- deep reinforcement learning (deep RL) -- which they believe also has vital implications for neuroscience and deserves more attention from neuroscientists. The first neuroscience applications of supervised deep learning can be traced back to the 1980s. The increasing availability of more powerful computers over the past decade has renewed research efforts in applying AI approaches -- especially supervised deep learning -- to neuroscience. Deep RL unites deep learning and reinforcement learning, a computational framework that has already had a substantial impact on neuroscience research.

As a basis for modelling brain function, deep learning has in recent years been used to model systems in vision, audition, motor control, navigation, and cognitive control. In a new paper, DeepMind researchers call attention to another "fundamentally novel" development in AI research -- deep reinforcement learning (deep RL) -- which they believe also has vital implications for neuroscience and deserves more attention from neuroscientists. The first neuroscience applications of supervised deep learning can be traced back to the 1980s. The increasing availability of more powerful computers over the past decade has renewed research efforts in applying AI approaches -- especially supervised deep learning -- to neuroscience.Deep RL unites deep learning and reinforcement learning, a computational framework that has already had a substantial impact on neuroscience research. The DeepMind team proposes deep RL as a comprehensive framework for studying the interplay between learning, representation, and decision-making that can bring new set of research tools and a wide range of novel hypotheses to the brain sciences.Although deep neural networks have proven an impressive model for neural representation, the team notes that related research has mostly utilized supervised training and has therefore provided little direct leverage on the big-picture problem of understanding motivated, goal-directed …