Beam search is the default decoding strategy for many sequence generation tasks in NLP. The set of approximate K-best items returned by the algorithm is a useful summary of the distribution for many applications; however, the candidates typically exhibit high overlap and may give a highly biased estimate for expectations under our model. These problems can be addressed by instead using stochastic decoding strategies. In this work, we propose a new method for turning beam search into a stochastic process: Conditional Poisson stochastic beam search. Rather than taking the maximizing set at each iteration, we sample K candidates without replacement according to the conditional Poisson sampling design. We view this as a more natural alternative to Kool et. al. 2019's stochastic beam search (SBS). Furthermore, we show how samples generated under the CPSBS design can be used to build consistent estimators and sample diverse sets from sequence models. In our experiments, we observe CPSBS produces lower variance and more efficient estimators than SBS, even showing improvements in high entropy settings.
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Statistical machine learning models trained with stochastic gradient algorithms are increasingly being deployed in critical scientific applications. However, computing the stochastic gradient in several such applications is highly expensive or even impossible at times. In such cases, derivative-free or zeroth-order algorithms are used. An important question which has thus far not been addressed sufficiently in the statistical machine learning literature is that of equipping stochastic zeroth-order algorithms with practical yet rigorous inferential capabilities so that we not only have point estimates or predictions but also quantify the associated uncertainty via confidence intervals or sets. Towards this, in this work, we first establish a central limit theorem for Polyak-Ruppert averaged stochastic zeroth-order gradient algorithm. We then provide online estimators of the asymptotic covariance matrix appearing in the central limit theorem, thereby providing a practical procedure for constructing asymptotically valid confidence sets (or intervals) for parameter estimation (or prediction) in the zeroth-order setting.
We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisson map property. For this purpose, we propose explicit stochastic Poisson integrators based on a splitting strategy, and analyse their qualitative and quantitative properties: preservation of Casimir functions, existence of almost sure or moment bounds, asymptotic preserving property, and strong and weak rates of convergence. The construction of the schemes and the theoretical results are illustrated through extensive numerical experiments for three examples of stochastic Lie--Poisson systems, namely: stochastically perturbed Maxwell--Bloch, rigid body and sine--Euler equations.
The estimation of Average Treatment Effect (ATE) as a causal parameter is carried out in two steps, where in the first step, the treatment and outcome are modeled to incorporate the potential confounders, and in the second step, the predictions are inserted into the ATE estimators such as the Augmented Inverse Probability Weighting (AIPW) estimator. Due to the concerns regarding the nonlinear or unknown relationships between confounders and the treatment and outcome, there has been an interest in applying non-parametric methods such as Machine Learning (ML) algorithms instead. Some literature proposes to use two separate Neural Networks (NNs) where there's no regularization on the network's parameters except the Stochastic Gradient Descent (SGD) in the NN's optimization. Our simulations indicate that the AIPW estimator suffers extensively if no regularization is utilized. We propose the normalization of AIPW (referred to as nAIPW) which can be helpful in some scenarios. nAIPW, provably, has the same properties as AIPW, that is, the double-robustness and orthogonality properties. Further, if the first step algorithms converge fast enough, under regulatory conditions, nAIPW will be asymptotically normal. We also compare the performance of AIPW and nAIPW in terms of the bias and variance when small to moderate L1 regularization is imposed on the NNs.
Queue length violation probability, i.e., the tail distribution of the queue length, is a widely used statistical quality-of-service (QoS) metric in wireless communications. Many previous works conducted tail distribution analysis on the control policies with the assumption that the condition of the large deviations theory (LDT) is satisfied. LDT indicates that the tail distribution of the queue length has a linear-decay-rate exponent. However, there are many control policies which do not meet that assumption, while the optimal control policy may be included in these policies. In this paper, we put our focus on the analysis of the tail distribution of the queue length from the perspective of cross-layer design in wireless link transmission. Specifically, we divide the wireless link transmission systems into three scenarios according to the decay rate of the queue-length tail distribution with the finite average power consumption. A heuristic policy is conceived to prove that the arbitrary-decay-rate tail distribution with the finite average power consumption exists in Rayleigh fading channels. Based on this heuristic policy, we generalize the analysis to Nakagami-m fading channels. Numerical results with approximation validate our analysis.
This paper investigates the problem of online statistical inference of model parameters in stochastic optimization problems via the Kiefer-Wolfowitz algorithm with random search directions. We first present the asymptotic distribution for the Polyak-Ruppert-averaging type Kiefer-Wolfowitz (AKW) estimators, whose asymptotic covariance matrices depend on the function-value query complexity and the distribution of search directions. The distributional result reflects the trade-off between statistical efficiency and function query complexity. We further analyze the choices of random search directions to minimize the asymptotic covariance matrix, and conclude that the optimal search direction depends on the optimality criteria with respect to different summary statistics of the Fisher information matrix. Based on the asymptotic distribution result, we conduct online statistical inference by providing two construction procedures of valid confidence intervals. We provide numerical experiments verifying our theoretical results with the practical effectiveness of the procedures.
The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.
Optimal transport distances have found many applications in machine learning for their capacity to compare non-parametric probability distributions. Yet their algorithmic complexity generally prevents their direct use on large scale datasets. Among the possible strategies to alleviate this issue, practitioners can rely on computing estimates of these distances over subsets of data, {\em i.e.} minibatches. While computationally appealing, we highlight in this paper some limits of this strategy, arguing it can lead to undesirable smoothing effects. As an alternative, we suggest that the same minibatch strategy coupled with unbalanced optimal transport can yield more robust behavior. We discuss the associated theoretical properties, such as unbiased estimators, existence of gradients and concentration bounds. Our experimental study shows that in challenging problems associated to domain adaptation, the use of unbalanced optimal transport leads to significantly better results, competing with or surpassing recent baselines.
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
Automatic neural architecture design has shown its potential in discovering powerful neural network architectures. Existing methods, no matter based on reinforcement learning or evolutionary algorithms (EA), conduct architecture search in a discrete space, which is highly inefficient. In this paper, we propose a simple and efficient method to automatic neural architecture design based on continuous optimization. We call this new approach neural architecture optimization (NAO). There are three key components in our proposed approach: (1) An encoder embeds/maps neural network architectures into a continuous space. (2) A predictor takes the continuous representation of a network as input and predicts its accuracy. (3) A decoder maps a continuous representation of a network back to its architecture. The performance predictor and the encoder enable us to perform gradient based optimization in the continuous space to find the embedding of a new architecture with potentially better accuracy. Such a better embedding is then decoded to a network by the decoder. Experiments show that the architecture discovered by our method is very competitive for image classification task on CIFAR-10 and language modeling task on PTB, outperforming or on par with the best results of previous architecture search methods with a significantly reduction of computational resources. Specifically we obtain $2.07\%$ test set error rate for CIFAR-10 image classification task and $55.9$ test set perplexity of PTB language modeling task. The best discovered architectures on both tasks are successfully transferred to other tasks such as CIFAR-100 and WikiText-2.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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