Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve Markov chain Monte Carlo sampling with limited applicability to large data sets. We extend some of these techniques to scale efficiently when the problem exhibits a sequential structure. We propose an approximation that enables sequential sampling of both latent variables and associated parameters. We demonstrate strong performance in growing-data settings tha…
We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construct a class of consistent adaptive policies, under which the average outcome converges with probability 1 to the true value under complete information for all distributions with finite means. We also compare the rate of convergence for various policies in this class using simulatio…
At the present time, sequential item recommendation models are compared by calculating metrics on a small item subset (target set) to speed up computation. The target set contains the relevant item and a set of negative items that are sampled from the full item set. Two well-known strategies to sample negative items are uniform random sampling and sampling by popularity to better approximate the item frequency distribution in the dataset. Most recently published papers on sequential item recommendation rely on sampling by popularity to compare the evaluated models. However, recent work has alr…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $θ$ common to all probability measures. Additionally, each process $i\in\{1, \dots, K\}$ has a private parameter $α_i$. The objective is to design an active sampling algorithm for sequentially estimating these parameters in order to form reliable estimates for all shared and private parameters with the fewest number of samples. This sampling algorithm has three key compon…
CNRS（法国国家科学研究中心）；Univ. Lille（里尔大学）；Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究院）；Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum mean among a finite set of distributions compares to a given threshold. We develop refined non-asymptotic lower bounds, which show that optimality mandates very different sampling behavior for a low vs high true minimum. We show that Thompson Sampling and the intuitive Lower Confidence Bounds policy each nail only one of these cases. We develop a novel appr…
Many modern sequential recommender systems use deep neural networks, which can effectively estimate the relevance of items but require a lot of time to train. Slow training increases expenses, hinders product development timescales and prevents the model from being regularly updated to adapt to changing user preferences. Training such sequential models involves appropriately sampling past user interactions to create a realistic training objective. The existing training objectives have limitations. For instance, next item prediction never uses the beginning of the sequence as a learning target,…
Lawrence Livermore National Laboratories（劳伦斯利弗莫尔国家实验室）
This paper provides a general framework to study the effect of sampling properties of training data on the generalization error of the learned machine learning (ML) models. Specifically, we propose a new spectral analysis of the generalization error, expressed in terms of the power spectra of the sampling pattern and the function involved. The framework is build in the Euclidean space using Fourier analysis and establishes a connection between some high dimensional geometric objects and optimal spectral form of different state-of-the-art sampling patterns. Subsequently, we estimate the expecte…
Northeastern University（东北大学）；University of Waterloo（滑铁卢大学）
Driven by the critical needs of biomanufacturing 4.0, we introduce a probabilistic knowledge graph hybrid model characterizing the risk- and science-based understanding of bioprocess mechanisms. It can faithfully capture the important properties, including nonlinear reactions, partially observed state, and nonstationary dynamics. Given very limited real process observations, we derive a posterior distribution quantifying model estimation uncertainty. To avoid the evaluation of intractable likelihoods, Approximate Bayesian Computation sampling with Sequential Monte Carlo (ABC-SMC) is utilized t…
Louisiana State University at Baton Rouge（巴吞鲁日路易斯安那州立大学）；Southern University and A&M College（南方大学及农工学院）
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level, it suffices to continue sampling until the sample sum is no less than a certain bound and then take the average of samples as an estimate for the mean of the bounded random variable. We have developed an explicit formula and a bisection search method for the determination of such bound of sample sum, without any knowledge of the bounded variable. Moreover, …
Thompson Sampling has generated significant interest due to its better empirical performance than upper confidence bound based algorithms. In this paper, we study Thompson Sampling based algorithm for Unsupervised Sequential Selection (USS) problem. The USS problem is a variant of the stochastic multi-armed bandits problem, where the loss of an arm can not be inferred from the observed feedback. In the USS setup, arms are associated with fixed costs and are ordered, forming a cascade. In each round, the learner selects an arm and observes the feedback from arms up to the selected arm. The lear…
Entity resolution (ER) presents unique challenges for evaluation methodology. While crowdsourcing platforms acquire ground truth, sound approaches to sampling must drive labelling efforts. In ER, extreme class imbalance between matching and non-matching records can lead to enormous labelling requirements when seeking statistically consistent estimates for rigorous evaluation. This paper addresses this important challenge with the OASIS algorithm: a sampler and F-measure estimator for ER evaluation. OASIS draws samples from a (biased) instrumental distribution, chosen to ensure estimators with …
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings, produce output samples drawn from a distribution that may be far from the target posterior distribution. This paper shows how to upper-bound the symmetric KL divergence between the output distribution of a broad class of sequential Monte Carlo (SMC) samplers and their target posterior distributions, subject to assumptions about the accuracy of a separate gold…
University of Chicago（芝加哥大学）；University of Cambridge（剑桥大学）
We propose a novel algorithm for sequential matrix completion in a recommender system setting, where the $(i,j)$th entry of the matrix corresponds to a user $i$'s rating of product $j$. The objective of the algorithm is to provide a sequential policy for user-product pair recommendation which will yield the highest possible ratings after a finite time horizon. The algorithm uses a Gamma process factor model with two posterior-focused bandit policies, Thompson Sampling and Information-Directed Sampling. While Thompson Sampling shows competitive performance in simulations, state-of-the-art perfo…
Sampling-based planning is the predominant paradigm for motion planning in robotics. Most sampling-based planners use a global random sampling scheme to guarantee probabilistic completeness. However, most schemes are often inefficient as the samples drawn from the global proposal distribution, and do not exploit relevant local structures. Local sampling-based motion planners, on the other hand, take sequential decisions of random walks to samples valid trajectories in configuration space. However, current approaches do not adapt their strategies according to the success and failures of past sa…
On the Impact of Sampling on Deep Sequential State Estimation
Northeastern University（东北大学）；CRAN, University of Lorraine, CNRS（洛林大学CRAN实验室，法国国家科学研究中心）；Institute for Experiential AI, Northeastern University（东北大学体验式人工智能研究所）
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the 'next-best' data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach utilizes Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf a…
