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Improved MDL Estimators Using Fiber Bundle of Local Exponential Families for Non-exponential Families
Minimum Description Length (MDL) estimators, using two-part codes for universal coding, are analyzed.
Complexity, Statistical Risk, and Metric Entropy of Deep Nets Using Total Path Variation
For any ReLU network there is a representation in which the sum of the absolute values of the weights into each node is exactly $1$, and the input layer variables are multiplied by a value $V$ coinciding with the total variation of the path weights.
Approximation and Estimation for High-Dimensional Deep Learning Networks
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations.
Minimax Lower Bounds for Ridge Combinations Including Neural Nets
Estimation of functions of $ d $ variables is considered using ridge combinations of the form $ \textstyle\sum_{k=1}^m c_{1, k} \phi(\textstyle\sum_{j=1}^d c_{0, j, k}x_j-b_k) $ where the activation function $ \phi $ is a function with bounded value and derivative.
Approximation by Combinations of ReLU and Squared ReLU Ridge Functions with $ \ell^1 $ and $ \ell^0 $ Controls
We establish $ L^{\infty} $ and $ L^2 $ error bounds for functions of many variables that are approximated by linear combinations of ReLU (rectified linear unit) and squared ReLU ridge functions with $ \ell^1 $ and $ \ell^0 $ controls on their inner and outer parameters.
Risk Bounds for High-dimensional Ridge Function Combinations Including Neural Networks
On the other hand, if the candidate fits are chosen from a discretization, we show that $ \mathbb{E}\|\hat{f} - f^{\star} \|^2 \leq \left(v^3_{f^{\star}}\frac{\log d}{n}\right)^{2/5} $.
