We present Shapeshifter Networks (SSNs), a flexible neural network framework that improves performance and reduces memory requirements on a diverse set of scenarios over standard neural networks. Our approach is based on the observation that many neural networks are severely overparameterized, resulting in significant waste in computational resources as well as being susceptible to overfitting. SSNs address this by learning where and how to share parameters between layers in a neural network while avoiding degenerate solutions that result in underfitting. Specifically, we automatically construct parameter groups that identify where parameter sharing is most beneficial. Then, we map each group's weights to construct layers with learned combinations of candidates from a shared parameter pool. SSNs can share parameters across layers even when they have different sizes, perform different operations, and/or operate on features from different modalities. We evaluate our approach on a diverse set of tasks, including image classification, bidirectional image-sentence retrieval, and phrase grounding, creating high performing models even when using as little as 1% of the parameters. We also apply SSNs to knowledge distillation, where we obtain state-of-the-art results when combined with traditional distillation methods.

The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold. Variational Autoencoders (VAEs) approximate this manifold by learning mappings from low-dimensional latent vectors to high-dimensional data while encouraging a global structure in the latent space through the use of a specified prior distribution. When this prior does not match the structure of the true data manifold, it can lead to a less accurate model of the data. To resolve this mismatch, we introduce the Variational Autoencoder with Learned Latent Structure (VAELLS) which incorporates a learnable manifold model into the latent space of a VAE. This enables us to learn the nonlinear manifold structure from the data and use that structure to define a prior in the latent space. The integration of a latent manifold model not only ensures that our prior is well-matched to the data, but also allows us to define generative transformation paths in the latent space and describe class manifolds by transformations stemming from examples of each class. We validate our model on examples with known latent structure and also demonstrate its capabilities on a real-world dataset.

This paper considers the estimation and prediction of a high-dimensional linear regression in the setting of transfer learning, using samples from the target model as well as auxiliary samples from different but possibly related regression models. When the set of "informative" auxiliary samples is known, an estimator and a predictor are proposed and their optimality is established. The optimal rates of convergence for prediction and estimation are faster than the corresponding rates without using the auxiliary samples. This implies that knowledge from the informative auxiliary samples can be transferred to improve the learning performance of the target problem. In the case that the set of informative auxiliary samples is unknown, we propose a data-driven procedure for transfer learning, called Trans-Lasso, and reveal its robustness to non-informative auxiliary samples and its efficiency in knowledge transfer. The proposed procedures are demonstrated in numerical studies and are applied to a dataset concerning the associations among gene expressions. It is shown that Trans-Lasso leads to improved performance in gene expression prediction in a target tissue by incorporating the data from multiple different tissues as auxiliary samples.

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization with Gaussian Processes (GPs). While this combination works well for unimodal target distributions, it is restricting the flexibility and applicability of Bayesian Optimization for accelerating likelihood-free inference more generally. We address this problem by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while adding computational overhead that remains negligible for computationally intensive simulators.

Recent work has shown that the prior over functions induced by a deep Bayesian neural network (BNN) behaves as a Gaussian process (GP) as the width of all layers becomes large. However, many BNN applications are concerned with the BNN function space posterior. While some empirical evidence of the posterior convergence was provided in the original works of Neal (1996) and Matthews et al. (2018), it is limited to small datasets or architectures due to the notorious difficulty of obtaining and verifying exactness of BNN posterior approximations. We provide the missing theoretical proof that the exact BNN posterior converges (weakly) to the one induced by the GP limit of the prior. For empirical validation, we show how to generate exact samples from a finite BNN on a small dataset via rejection sampling.

There is a growing amount of literature on the relationship between wide neural networks (NNs) and Gaussian processes (GPs), identifying an equivalence between the two for a variety of NN architectures. This equivalence enables, for instance, accurate approximation of the behaviour of wide Bayesian NNs without MCMC or variational approximations, or characterisation of the distribution of randomly initialised wide NNs optimised by gradient descent without ever running an optimiser. We provide a rigorous extension of these results to NNs involving attention layers, showing that unlike single-head attention, which induces non-Gaussian behaviour, multi-head attention architectures behave as GPs as the number of heads tends to infinity. We further discuss the effects of positional encodings and layer normalisation, and propose modifications of the attention mechanism which lead to improved results for both finite and infinitely wide NNs. We evaluate attention kernels empirically, leading to a moderate improvement upon the previous state-of-the-art on CIFAR-10 for GPs without trainable kernels and advanced data preprocessing. Finally, we introduce new features to the Neural Tangents library (Novak et al., 2020) allowing applications of NNGP/NTK models, with and without attention, to variable-length sequences, with an example on the IMDb reviews dataset.

We propose a novel approach for a machine-learning-based detection of the type Ia supernovae using photometric information. Unlike other approaches, only real observation data is used during training. Despite being trained on a relatively small sample, the method shows good results on real data from the Open Supernovae Catalog. We also demonstrate that the quality of a model, trained on PLASTiCC simulated sample, significantly decreases evaluated on real objects.

From earth system sciences to climate modeling and ecology, many of the greatest empirical modeling challenges are geographic in nature. As these processes are characterized by spatial dynamics, we can exploit their autoregressive nature to inform learning algorithms. We introduce SXL, a method for learning with geospatial data using explicitly spatial auxiliary tasks. We embed the local Moran's I, a well-established measure of local spatial autocorrelation, into the training process, "nudging" the model to learn the direction and magnitude of local autoregressive effects in parallel with the primary task. Further, we propose an expansion of Moran's I to multiple resolutions to capture effects at different spatial granularities and over varying distance scales. We show the superiority of this method for training deep neural networks using experiments with real-world geospatial data in both generative and predictive modeling tasks. Our approach can be used with arbitrary network architectures and, in our experiments, consistently improves their performance. We also outperform appropriate, domain-specific interpolation benchmarks. Our work highlights how integrating the geographic information sciences and spatial statistics into machine learning models can address the specific challenges of spatial data.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

In this paper we propose novel distributed gradient-based temporal difference algorithms for multi-agent off-policy learning of linear approximation of the value function in Markov decision processes. The algorithms are composed of: 1) local parameter updates based on the single-agent off-policy gradient temporal difference learning algorithms, including eligibility traces with state dependent parameters, and 2) linear dynamic consensus scheme over the underlying, typically sparsely connected, inter-agent communication network. The proposed algorithms differ in the way of how the time-scales are selected, how local recursions are performed and how consensus iterations are incorporated. The algorithms are completely decentralized, allowing applications in which all the agents may have completely different behavior policies while evaluating a single target policy. In this sense, the algorithms may be considered as a tool for either parallelization or multi-agent collaborative learning under given constraints. We provide weak convergence results, taking rigorously into account properties of the underlying Feller-Markov processes. We prove that, under nonrestrictive assumptions on the time-varying network topology and the individual state-visiting distributions of the agents, the parameter estimates of the algorithms weakly converge to a consensus point. The variance reduction effect of the proposed algorithms is demonstrated by analyzing a limiting stochastic differential equation. Specific guidelines for network design, providing the desired convergence points, are given. The algorithms' properties are illustrated by characteristic simulation results.