Recent years have seen the proposal of a number of neural architectures for the problem of Program Induction. Given a set of input-output examples, these architectures are able to learn mappings that generalize to new test inputs. While achieving impressive results, these approaches have a number of important limitations: (a) they are computationally expensive and hard to train, (b) a model has to be trained for each task (program) separately, and (c) it is hard to interpret or verify the correctness of the learnt mapping (as it is defined by a neural network). In this paper, we propose a novel technique, Neuro-Symbolic Program Synthesis, to overcome the above-mentioned problems. Once trained, our approach can automatically construct computer programs in a domain-specific language that are consistent with a set of input-output examples provided at test time. Our method is based on two novel neural modules. The first module, called the cross correlation I/O network, given a set of input-output examples, produces a continuous representation of the set of I/O examples. The second module, the Recursive-Reverse-Recursive Neural Network (R3NN), given the continuous representation of the examples, synthesizes a program by incrementally expanding partial programs. We demonstrate the effectiveness of our approach by applying it to the rich and complex domain of regular expression based string transformations. Experiments show that the R3NN model is not only able to construct programs from new input-output examples, but it is also able to construct new programs for tasks that it had never observed before during training.
Crowdsourcing has become a primary means for label collection in many real-world machine learning applications. A classical method for inferring the true labels from the noisy labels provided by crowdsourcing workers is Dawid-Skene estimator. In this paper, we prove convergence rates of a projected EM algorithm for the Dawid-Skene estimator. The revealed exponent in the rate of convergence is shown to be optimal via a lower bound argument. Our work resolves the long standing issue of whether Dawid-Skene estimator has sound theoretical guarantees besides its good performance observed in practice. In addition, a comparative study with majority voting illustrates both advantages and pitfalls of the Dawid-Skene estimator.
In many machine learning applications, crowdsourcing has become the primary means for label collection. In this paper, we study the optimal error rate for aggregating labels provided by a set of non-expert workers. Under the classic Dawid-Skene model, we establish matching upper and lower bounds with an exact exponent $mI(\pi)$ in which $m$ is the number of workers and $I(\pi)$ the average Chernoff information that characterizes the workers' collective ability. Such an exact characterization of the error exponent allows us to state a precise sample size requirement $m>\frac{1}{I(\pi)}\log\frac{1}{\epsilon}$ in order to achieve an $\epsilon$ misclassification error. In addition, our results imply the optimality of various EM algorithms for crowdsourcing initialized by consistent estimators.
Crowdsourcing has gained immense popularity in machine learning applications for obtaining large amounts of labeled data. Crowdsourcing is cheap and fast, but suffers from the problem of low-quality data. To address this fundamental challenge in crowdsourcing, we propose a simple payment mechanism to incentivize workers to answer only the questions that they are sure of and skip the rest. We show that surprisingly, under a mild and natural "no-free-lunch" requirement, this mechanism is the one and only incentive-compatible payment mechanism possible. We also show that among all possible incentive-compatible mechanisms (that may or may not satisfy no-free-lunch), our mechanism makes the smallest possible payment to spammers. We further extend our results to a more general setting in which workers are required to provide a quantized confidence for each question. Interestingly, this unique mechanism takes a "multiplicative" form. The simplicity of the mechanism is an added benefit. In preliminary experiments involving over 900 worker-task pairs, we observe a significant drop in the error rates under this unique mechanism for the same or lower monetary expenditure.
The growing need for labeled training data has made crowdsourcing an important part of machine learning. The quality of crowdsourced labels is, however, adversely affected by three factors: (1) the workers are not experts; (2) the incentives of the workers are not aligned with those of the requesters; and (3) the interface does not allow workers to convey their knowledge accurately, by forcing them to make a single choice among a set of options. In this paper, we address these issues by introducing approval voting to utilize the expertise of workers who have partial knowledge of the true answer, and coupling it with a ("strictly proper") incentive-compatible compensation mechanism. We show rigorous theoretical guarantees of optimality of our mechanism together with a simple axiomatic characterization. We also conduct preliminary empirical studies on Amazon Mechanical Turk which validate our approach.
There is a rapidly increasing interest in crowdsourcing for data labeling. By crowdsourcing, a large number of labels can be often quickly gathered at low cost. However, the labels provided by the crowdsourcing workers are usually not of high quality. In this paper, we propose a minimax conditional entropy principle to infer ground truth from noisy crowdsourced labels. Under this principle, we derive a unique probabilistic labeling model jointly parameterized by worker ability and item difficulty. We also propose an objective measurement principle, and show that our method is the only method which satisfies this objective measurement principle. We validate our method through a variety of real crowdsourcing datasets with binary, multiclass or ordinal labels.
Human computation or crowdsourcing involves joint inference of the ground-truth-answers and the worker-abilities by optimizing an objective function, for instance, by maximizing the data likelihood based on an assumed underlying model. A variety of methods have been proposed in the literature to address this inference problem. As far as we know, none of the objective functions in existing methods is convex. In machine learning and applied statistics, a convex function such as the objective function of support vector machines (SVMs) is generally preferred, since it can leverage the high-performance algorithms and rigorous guarantees established in the extensive literature on convex optimization. One may thus wonder if there exists a meaningful convex objective function for the inference problem in human computation. In this paper, we investigate this convexity issue for human computation. We take an axiomatic approach by formulating a set of axioms that impose two mild and natural assumptions on the objective function for the inference. Under these axioms, we show that it is unfortunately impossible to ensure convexity of the inference problem. On the other hand, we show that interestingly, in the absence of a requirement to model "spammers", one can construct reasonable objective functions for crowdsourcing that guarantee convex inference.
Crowdsourcing is a popular paradigm for effectively collecting labels at low cost. The Dawid-Skene estimator has been widely used for inferring the true labels from the noisy labels provided by non-expert crowdsourcing workers. However, since the estimator maximizes a non-convex log-likelihood function, it is hard to theoretically justify its performance. In this paper, we propose a two-stage efficient algorithm for multi-class crowd labeling problems. The first stage uses the spectral method to obtain an initial estimate of parameters. Then the second stage refines the estimation by optimizing the objective function of the Dawid-Skene estimator via the EM algorithm. We show that our algorithm achieves the optimal convergence rate up to a logarithmic factor. We conduct extensive experiments on synthetic and real datasets. Experimental results demonstrate that the proposed algorithm is comparable to the most accurate empirical approach, while outperforming several other recently proposed methods.
In crowd labeling, a large amount of unlabeled data instances are outsourced to a crowd of workers. Workers will be paid for each label they provide, but the labeling requester usually has only a limited amount of the budget. Since data instances have different levels of labeling difficulty and workers have different reliability, it is desirable to have an optimal policy to allocate the budget among all instance-worker pairs such that the overall labeling accuracy is maximized. We consider categorical labeling tasks and formulate the budget allocation problem as a Bayesian Markov decision process (MDP), which simultaneously conducts learning and decision making. Using the dynamic programming (DP) recurrence, one can obtain the optimal allocation policy. However, DP quickly becomes computationally intractable when the size of the problem increases. To solve this challenge, we propose a computationally efficient approximate policy, called optimistic knowledge gradient policy. Our MDP is a quite general framework, which applies to both pull crowdsourcing marketplaces with homogeneous workers and push marketplaces with heterogeneous workers. It can also incorporate the contextual information of instances when they are available. The experiments on both simulated and real data show that the proposed policy achieves a higher labeling accuracy than other existing policies at the same budget level.
Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be applied to analyze many common prediction methods, including the majority voting and weighted majority voting. These bound results could be useful for controlling the error rate and designing better algorithms. We show that the oracle Maximum A Posterior (MAP) rule approximately optimizes our upper bound on the mean error rate for any hyperplane binary labeling rule, and propose a simple data-driven weighted majority voting (WMV) rule (called one-step WMV) that attempts to approximate the oracle MAP and has a provable theoretical guarantee on the error rate. Moreover, we use simulated and real data to demonstrate that the data-driven EM-MAP rule is a good approximation to the oracle MAP rule, and to demonstrate that the mean error rate of the data-driven EM-MAP rule is also bounded by the mean error rate bound of the oracle MAP rule with estimated parameters plugging into the bound.