3260 papers • 126 benchmarks • 313 datasets
Gaussian Processes is a powerful framework for several machine learning tasks such as regression, classification and inference. Given a finite set of input output training data that is generated out of a fixed (but possibly unknown) function, the framework models the unknown function as a stochastic process such that the training outputs are a finite number of jointly Gaussian random variables, whose properties can then be used to infer the statistics (the mean and variance) of the function at test values of input. Source: Sequential Randomized Matrix Factorization for Gaussian Processes: Efficient Predictions and Hyper-parameter Optimization
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A new theoretical framework is developed casting dropout training in deep neural networks (NNs) as approximate Bayesian inference in deep Gaussian processes, which mitigates the problem of representing uncertainty in deep learning without sacrificing either computational complexity or test accuracy.
Stochastic variational inference for Gaussian process models is introduced and it is shown how GPs can be variationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform Variational inference.
Conditional Neural Processes are inspired by the flexibility of stochastic processes such as GPs, but are structured as neural networks and trained via gradient descent, yet scale to complex functions and large datasets.
The exact equivalence between infinitely wide deep networks and GPs is derived and it is found that test performance increases as finite-width trained networks are made wider and more similar to a GP, and thus that GP predictions typically outperform those of finite- width networks.
This work presents a doubly stochastic variational inference algorithm, which does not force independence between layers in Deep Gaussian processes, and provides strong empirical evidence that the inference scheme for DGPs works well in practice in both classification and regression.
It is proved that the evolution of an ANN during training can also be described by a kernel: during gradient descent on the parameters of anANN, the network function follows the so-called kernel gradient associated with a new object, which is called the Neural Tangent Kernel (NTK).
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a deep architecture, using local kernel interpolation, inducing points, and structure exploiting (Kronecker and Toeplitz) algebra for a scalable kernel representation. These closed-form kernels can be used as drop-in replacements for standard kernels, with benefits in expressive power and scalability. We jointly learn the properties of these kernels through the marginal likelihood of a Gaussian process. Inference and learning cost $O(n)$ for $n$ training points, and predictions cost $O(1)$ per test point. On a large and diverse collection of applications, including a dataset with 2 million examples, we show improved performance over scalable Gaussian processes with flexible kernel learning models, and stand-alone deep architectures.
Adversarial Robustness Toolbox is a Python library supporting developers and researchers in defending Machine Learning models against adversarial threats and helps making AI systems more secure and trustworthy.
This work identifies a decomposition of Gaussian processes that naturally lends itself to scalable sampling by separating out the prior from the data, and proposes an easy-to-use and general-purpose approach for fast posterior sampling, which seamlessly pairs with sparse approximations to afford scalability both during training and at test time.
This monograph reviews different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
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