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Register a new userA Tale of Two Efficient and Informative Negative Sampling Distributions
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Added by
Shabnam Daghaghi
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Softmax classifiers with a very large number of classes naturally occur in many applications such as natural language processing and information retrieval. The calculation of full softmax is costly from the computational and energy perspective. There have been various sampling approaches to overcome this challenge, popularly known as negative sampling (NS). Ideally, NS should sample negative classes from a distribution that is dependent on the input data, the current parameters, and the correct positive class. Unfortunately, due to the dynamically updated parameters and data samples, there is no sampling scheme that is provably adaptive and samples the negative classes efficiently. Therefore, alternative heuristics like random sampling, static frequency-based sampling, or learning-based biased sampling, which primarily trade either the sampling cost or the adaptivity of samples per iteration are adopted. In this paper, we show two classes of distributions where the sampling scheme is truly adaptive and provably generates negative samples in near-constant time. Our implementation in C++ on CPU is significantly superior, both in terms of wall-clock time and accuracy, compared to the most optimized TensorFlow implementations of other popular negative sampling approaches on powerful NVIDIA V100 GPU.
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Negative sampling, which samples negative triplets from non-observed ones in knowledge graph (KG), is an essential step in KG embedding. Recently, generative adversarial network (GAN), has been introduced in negative sampling. By sampling negative triplets with large gradients, these methods avoid the problem of vanishing gradient and thus obtain better performance. However, they make the original model more complex and harder to train. In this paper, motivated by the observation that negative triplets with large gradients are important but rare, we propose to directly keep track of them with the cache. In this way, our method acts as a distilled version of previous GAN-based methods, which does not waste training time on additional parameters to fit the full distribution of negative triplets. However, how to sample from and update the cache are two critical questions. We propose to solve these issues by automated machine learning techniques. The automated version also covers GAN-based methods as special cases. Theoretical explanation of NSCaching is also provided, justifying the superior over fixed sampling scheme. Besides, we further extend NSCaching with skip-gram model for graph embedding. Finally, extensive experiments show that our method can gain significant improvements on various KG embedding models and the skip-gram model, and outperforms the state-of-the-art negative sampling methods.
In multi-agent reinforcement learning, the inherent non-stationarity of the environment caused by other agents actions posed significant difficulties for an agent to learn a good policy independently. One way to deal with non-stationarity is agent modeling, by which the agent takes into consideration the influence of other agents policies. Most existing work relies on predicting other agents actions or goals, or discriminating between their policies. However, such modeling fails to capture the similarities and differences between policies simultaneously and thus cannot provide useful information when generalizing to unseen policies. To address this, we propose a general method to learn representations of other agents policies via the joint-action distributions sampled in interactions. The similarities and differences between policies are naturally captured by the policy distance inferred from the joint-action distributions and deliberately reflected in the learned representations. Agents conditioned on the policy representations can well generalize to unseen agents. We empirically demonstrate that our method outperforms existing work in multi-agent tasks when facing unseen agents.
Path representations are critical in a variety of transportation applications, such as estimating path ranking in path recommendation systems and estimating path travel time in navigation systems. Existing studies often learn task-specific path representations in a supervised manner, which require a large amount of labeled training data and generalize poorly to other tasks. We propose an unsupervised learning framework Path InfoMax (PIM) to learn generic path representations that work for different downstream tasks. We first propose a curriculum negative sampling method, for each input path, to generate a small amount of negative paths, by following the principles of curriculum learning. Next, emph{PIM} employs mutual information maximization to learn path representations from both a global and a local view. In the global view, PIM distinguishes the representations of the input paths from those of the negative paths. In the local view, emph{PIM} distinguishes the input path representations from the representations of the nodes that appear only in the negative paths. This enables the learned path representations to encode both global and local information at different scales. Extensive experiments on two downstream tasks, ranking score estimation and travel time estimation, using two road network datasets suggest that PIM significantly outperforms other unsupervised methods and is also able to be used as a pre-training method to enhance supervised path representation learning.
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from distribution D and subsequently corrupted on some fraction of points, our algorithm outputs a linear function whose squared error is close to the squared error of the best-fitting linear function with respect to D, assuming that the marginal distribution of D over the input space is emph{certifiably hypercontractive}. This natural property is satisfied by many well-studied distributions such as Gaussian, strongly log-concave distributions and, uniform distribution on the hypercube among others. We also give a simple statistical lower bound showing that some distributional assumption is necessary to succeed in this setting. These results are the first of their kind and were not known to be even information-theoretically possible prior to our work. Our approach is based on the sum-of-squares (SoS) method and is inspired by the recent applications of the method for parameter recovery problems in unsupervised learning. Our algorithm can be seen as a natural convex relaxation of the following conceptually simple non-convex optimization problem: find a linear function and a large subset of the input corrupted sample such that the least squares loss of the function over the subset is minimized over all possible large subsets.
Large machine learning models achieve unprecedented performance on various tasks and have evolved as the go-to technique. However, deploying these compute and memory hungry models on resource constraint environments poses new challenges. In this work, we propose mathematically provable Representer Sketch, a concise set of count arrays that can approximate the inference procedure with simple hashing computations and aggregations. Representer Sketch builds upon the popular Representer Theorem from kernel literature, hence the name, providing a generic fundamental alternative to the problem of efficient inference that goes beyond the popular approach such as quantization, iterative pruning and knowledge distillation. A neural network function is transformed to its weighted kernel density representation, which can be very efficiently estimated with our sketching algorithm. Empirically, we show that Representer Sketch achieves up to 114x reduction in storage requirement and 59x reduction in computation complexity without any drop in accuracy.
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