COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Statistical theory for deep neural networks with ReLU activation function

## Statistical theory for deep neural networks with ReLU activation functionAdd to your list(s) Download to your calendar using vCal - Johannes Schmidt-hieber (Universiteit Leiden)
- Wednesday 21 March 2018, 11:30-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. STSW02 - Statistics of geometric features and new data types The universal approximation theorem states that neural networks are capable of approximating any continuous function up to a small error that depends on the size of the network. The expressive power of a network does, however, not guarantee that deep networks perform well on data. For that, control of the statistical estimation risk is needed. In the talk, we derive statistical theory for fitting deep neural networks to data generated from the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve the minimax rates of convergence (up to logarithmic factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the n etwork. Specifically, we consider large networks with number of potential parameters being much bigger than the sample size. Interestingly, the depth (number of layers) of the neural network architectures plays an important role and our theory suggests that scaling the network depth with the logarithm of the sample size is natural. - https://arxiv.org/abs/1708.06633 – Article
This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsPolitics and Paradoxes of Transparency CRASSH Research Group Type the title of a new list here Trinity Hall Natural Sciences Society## Other talksCellular recycling: role of autophagy in aging and disease How archaeologists resolve the inductive risk argument Ethics for the working mathematician, seminar 10: Mathematicians being leaders. Beacon Salon # 8 The Dawn of the Antibiotic Age The Digital Railway - Network Rail Certified dimension reduction of the input parameter space of vector-valued functions |