We introduce a new method for estimating the parameter of the bivariate Clayton copulas within the framework of Algorithmic Inference. The method consists of a variant of the standard boot-strapping procedure for inferring random parameters, which we expressly devise to bypass the two pitfalls of this specific instance: the non independence of the Kendall statistics, customarily at the basis of this inference task, and the absence of a sufficient statistic w.r.t. \alpha. The variant is rooted on a numerical procedure in order to find the \alpha estimate at a fixed point of an iterative routine. Although paired with the customary complexity of the program which computes them, numerical results show an outperforming accuracy of the estimates.

Kernel learning methods are among the most effective learning methods and have been vigorously studied in the past decades. However, when tackling with complicated tasks, classical kernel methods are not flexible or "rich" enough to describe the data and hence could not yield satisfactory performance. In this paper, via Random Fourier Features (RFF), we successfully incorporate the deep architecture into kernel learning, which significantly boosts the flexibility and richness of kernel machines while keeps kernels' advantage of pairwise handling small data. With RFF, we could establish a deep structure and make every kernel in RFF layers could be trained end-to-end. Since RFF with different distributions could represent different kernels, our model has the capability of finding suitable kernels for each layer, which is much more flexible than traditional kernel-based methods where the kernel is pre-selected. This fact also helps yield a more sophisticated kernel cascade connection in the architecture. On small datasets (less than 1000 samples), for which deep learning is generally not suitable due to overfitting, our method achieves superior performance compared to advanced kernel methods. On large-scale datasets, including non-image and image classification tasks, our method also has competitive performance.

Modern neural networks are increasingly bottlenecked by the limited capacity of on-device GPU memory. Prior work explores dropping activations as a strategy to scale to larger neural networks under memory constraints. However, these heuristics assume uniform per-layer costs and are limited to simple architectures with linear graphs, limiting their usability. In this paper, we formalize the problem of trading-off DNN training time and memory requirements as the tensor rematerialization optimization problem, a generalization of prior checkpointing strategies. We introduce Checkmate, a system that solves for optimal schedules in reasonable times (under an hour) using off-the-shelf MILP solvers, then uses these schedules to accelerate millions of training iterations. Our method scales to complex, realistic architectures and is hardware-aware through the use of accelerator-specific, profile-based cost models. In addition to reducing training cost, Checkmate enables real-world networks to be trained with up to 5.1$\times$ larger input sizes.

From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly in the hypergraph context, despite a large body of prior work that has shown the utility of deep learning over graphs and sets. Building upon these recent advances, we propose \textit{Deep Hyperedges} (DHE), a modular framework that jointly uses contextual and permutation-invariant vertex membership properties of hyperedges in hypergraphs to perform classification and regression in transductive and inductive learning settings. In our experiments, we use a novel random walk procedure and show that our model achieves and, in most cases, surpasses state-of-the-art performance on benchmark datasets. Additionally, we study our framework's performance on a variety of diverse, non-standard hypergraph datasets and propose several avenues of future work to further enhance DHE.

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust and efficient measures of uncertainty are crucial. While it is possible to train regression networks to output the parameters of a probability distribution by maximizing a Gaussian likelihood function, the resulting model remains oblivious to the underlying confidence of its predictions. In this paper, we propose a novel method for training deterministic NNs to not only estimate the desired target but also the associated evidence in support of that target. We accomplish this by placing evidential priors over our original Gaussian likelihood function and training our NN to infer the hyperparameters of our evidential distribution. We impose priors during training such that the model is penalized when its predicted evidence is not aligned with the correct output. Thus the model estimates not only the probabilistic mean and variance of our target but also the underlying uncertainty associated with each of those parameters. We observe that our evidential regression method learns well-calibrated measures of uncertainty on various benchmarks, scales to complex computer vision tasks, and is robust to adversarial input perturbations.

This paper proposes an improved design of the perceptron unit to mitigate the vanishing gradient problem. This nuisance appears when training deep multilayer perceptron networks with bounded activation functions. The new neuron design, named auto-rotating perceptron (ARP), has a mechanism to ensure that the node always operates in the dynamic region of the activation function, by avoiding saturation of the perceptron. The proposed method does not change the inference structure learned at each neuron. We test the effect of using ARP units in some network architectures which use the sigmoid activation function. The results support our hypothesis that neural networks with ARP units can achieve better learning performance than equivalent models with classic perceptrons.

Gaining more comprehensive knowledge about drug-drug interactions (DDIs) is one of the most important tasks in drug development and medical practice. Recently graph neural networks have achieved great success in this task by modeling drugs as nodes and drug-drug interactions as links and casting DDI predictions as link prediction problems. However, correlations between link labels (e.g., DDI types) were rarely considered in existing works. We propose the graph energy neural network ( GENN) to explicitly model link type correlations. We formulate the DDI prediction task as a structure prediction problem, and introduce a new energy-based model where the energy function is defined by graph neural networks. Experiments on two real world DDI datasets demonstrated that GENN is superior to many baselines without consideration of link type correlations and achieved 13. 77% and 5.01% PR-AUC improvement on the two datasets, respectively. We also present a case study in which GENN can better capture meaningful DDI correlations compared with baseline models. The use of drug combinations is common and often necessary for treating patients with complex diseases.

Training large DL models with billions and potentially trillions of parameters is challenging. Existing solutions exhibit fundamental limitations to obtain both memory and scaling (computation/communication) efficiency together. Data parallelism does not help reduce memory footprint per device: a model with 1.5 billion parameters or more runs out of memory. Model parallelism hardly scales efficiently beyond multiple devices of a single node due to fine-grained computation and expensive communication. We develop a novel solution, Zero Redundancy Optimizer (ZeRO), to optimize memory, achieving both memory efficiency and scaling efficiency. Unlike basic data parallelism where memory states are replicated across data-parallel processes, ZeRO partitions model states instead, to scale the model size linearly with the number of devices. Furthermore, it retains scaling efficiency via computation and communication rescheduling and by reducing the model parallelism degree required to run large models. Our analysis on memory requirements and communication volume demonstrates: ZeRO has the potential to scale beyond 1 Trillion parameters using today's hardware (e.g., 1024 GPUs, 64 DGX-2 nodes). To meet near-term scaling goals and serve as a demonstration of ZeRO's capability, we implemented stage-1 optimizations of ZeRO (out of 3 stages in total described in the paper) and tested this ZeRO-OS version. ZeRO-OS reduces memory and boosts model size by 4x compared with the state-of-art, scaling up to 100B parameters. Moving forward, we will work on unlocking stage-2 optimizations, with up to 8x memory savings per device, and ultimately stage-3 optimizations, reducing memory linearly with respect to the number of devices and potentially scaling to models of arbitrary size. We are excited to transform very large models from impossible to train to feasible and efficient to train!

In this paper, we give a formalization of this shared pattern, which we call G IMLI, prove its general requirements, and derive a general-purpose algorithm for implementing similar approaches. Based on this analysis and algorithm, we describe a library of our design, higher, which we share with the community to assist and enable future research into these kinds of meta-learning approaches. We end the paper by showcasing the practical applications of this framework and library through illustrative experiments and ablation studies which they facilitate. 1 I NTRODUCTION Although it is by no means a new subfield of machine learning research (see e.g. Schmidhuber, 1987; Bengio, 2000; Hochreiter et al., 2001), there has recently been a surge of interest in meta-learning (e.g. This is due to the methods meta-learning provides, amongst other things, for producing models that perform well beyond the confines of a single task, outside the constraints of a static dataset, or simply with greater data efficiency or sample complexity. Due to the wealth of options in what could be considered "meta-" to a learning problem, the term itself may have been used with some degree of underspecification. However, it turns out that many meta-learning approaches, in particular in the recent literature, follow the pattern of optimizing the "meta-parameters" of the training process by nesting one or more inner loops in an outer training loop. Such nesting enables training a model for several steps, evaluating it, calculating or approximating the gradients of that evaluation with respect to the meta-parameters, and subsequently updating these meta-parameters.

In this paper, we aim to develop a simple and scalable reinforcement learning algorithm that uses standard supervised learning methods as subroutines. Our goal is an algorithm that utilizes only simple and convergent maximum likelihood loss functions, while also being able to leverage off-policy data. Our proposed approach, which we refer to as advantage-weighted regression (AWR), consists of two standard supervised learning steps: one to regress onto target values for a value function, and another to regress onto weighted target actions for the policy. The method is simple and general, can accommodate continuous and discrete actions, and can be implemented in just a few lines of code on top of standard supervised learning methods. We provide a theoretical motivation for AWR and analyze its properties when incorporating off-policy data from experience replay. We evaluate AWR on a suite of standard OpenAI Gym benchmark tasks, and show that it achieves competitive performance compared to a number of well-established state-of-the-art RL algorithms. AWR is also able to acquire more effective policies than most off-policy algorithms when learning from purely static datasets with no additional environmental interactions. Furthermore, we demonstrate our algorithm on challenging continuous control tasks with highly complex simulated characters.