Noisy Oracle Research Articles

Almost exact recovery in noisy semi-supervised learning

Abstract Graph-based semi-supervised learning methods combine the graph structure and labeled data to classify unlabeled data. In this work, we study the effect of a noisy oracle on classification. In particular, we derive the maximum a posteriori (MAP) estimator for clustering a degree corrected stochastic block model when a noisy oracle reveals a fraction of the labels. We then propose an algorithm derived from a continuous relaxation of the MAP, and we establish its consistency. Numerical experiments show that our approach achieves promising performance on synthetic and real data sets, even in the case of very noisy labeled data.

A non-monotone trust-region method with noisy oracles and additional sampling

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies that yield noisy approximations of the finite sum objective function and its gradient. We introduce an adaptive sample size strategy based on inexpensive additional sampling to control the resulting approximation error. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations.

First- and second-order high probability complexity bounds for trust-region methods with noisy oracles

First- and second-order high probability complexity bounds for trust-region methods with noisy oracles

Sample complexity of rank regression using pairwise comparisons

We consider a rank regression setting, in which a dataset of N samples with features in Rd is ranked by an oracle via M pairwise comparisons. Specifically, there exists a latent total ordering of the samples; when presented with a pair of samples, a noisy oracle identifies the one ranked higher with respect to the underlying total ordering. A learner observes a dataset of such comparisons and wishes to regress sample ranks from their features. We show that to learn the model parameters with ϵ>0 accuracy, it suffices to conduct M∈Ω(dNlog3N/ϵ2) comparisons uniformly at random when N is Ω(d/ϵ2).

Loss-based active learning via double-branch deep network

Due to the limitation of data annotation and the ability of dealing with label-efficient problems, active learning has received lots of research interest in recent years. Most of the existing approaches focus on designing a different selection strategy to achieve better performance for special tasks; however, the performance of the strategy still needs to be improved. In this work, we focus on improving the performance of active learning and propose a loss-based strategy that learns to predict target losses of unlabeled inputs to select the most uncertain samples, which is designed to learn a better selection strategy based on a double-branch deep network. Experimental results on two visual recognition tasks show that our approach achieves the state-of-the-art performance compared with previous methods. Moreover, our approach is also robust to different network architectures, biased initial labels, noisy oracles, or sampling budget sizes, and the complexity is also competitive, which demonstrates the effectiveness and efficiency of our proposed approach.

Joint Alignment From Pairwise Differences with a Noisy Oracle

In this work we consider the problem of recovering $n$ discrete random variables $x_i\in \{0,\ldots,k-1\}, 1 \leq i \leq n$ (where $k$ is constant) with the smallest possible number of queries to a noisy oracle that returns for a given query pair $(x_i,x_j)$ a noisy measurement of their modulo $k$ pairwise difference, i.e., $y_{ij} = (x_i-x_j) \mod k$. This is a joint discrete alignment problem with important applications in computer vision, graph mining, and spectroscopy imaging. Our main result is a polynomial time algorithm that learns exactly with high probability the alignment (up to some unrecoverable offset) using $O(n^{1+o(1)})$ queries.

Probabilistic bisection with spatial metamodels

Probabilistic Bisection Algorithms perform root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed simultaneously. To this end, we propose to leverage the spatial structure of a typical oracle by constructing a statistical surrogate for the underlying logistic regression step. We investigate several surrogates, including Binomial Gaussian Processes (B-GP), Polynomial, Kernel, and Spline Logistic Regression. In parallel, we develop sampling policies that adaptively balance learning the oracle distribution and learning the root. One of our proposals mimics active learning with B-GPs and provides a novel look-ahead predictive variance formula. The resulting gains of our Spatial PBA algorithm relative to earlier G-PBA models are illustrated with synthetic examples and a challenging stochastic root finding problem from Bermudan option pricing.

On semi-supervised active clustering of stable instances with oracles

We consider the problem of semi-supervised active clustering under multiplicative perturbation stability with respect to the distance function. Stable instances have an optimal solution that does not change when the distances are perturbed. This captures the notion that the optimal solution is tolerant to measurement errors and uncertainty in the points. Semi-supervision allows us to have an oracle O which answers pairwise queries. We design efficient algorithms to solve problems of multiplicative perturbation stability for semi-supervised clustering by using an ideal as well as a noisy oracle model. We present theoretical performance guarantee of the algorithms.

Iterative Classroom Teaching

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O(min{d,N}log 1/ɛ) exam-ples, where d is the ambient dimension of the problem, N is the number of learners, and ɛ is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners’ internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners’ workload and the teacher’s cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Sensitivity of quantum speedup by quantum annealing to a noisy oracle

The glued-trees problem is the only example known to date for which quantum annealing provides an exponential speedup, albeit by partly using excited state evolution, in an oracular setting. How robust is this speedup to noise on the oracle? To answer this, we construct phenomenological short-range and long-range noise models, and noise models that break or preserve the reflection symmetry of the spectrum. We show that under the long-range noise models an exponential quantum speedup is retained. However, we argue that a classical algorithm with an equivalent long-range noise model also exhibits an exponential speedup over the noiseless model. In the quantum setting the long-range noise is able to lift the spectral gap of the problem so that the evolution changes from diabatic to adiabatic. In the classical setting, long-range noise creates a significant probability of the walker landing directly on the EXIT vertex. Under short-range noise the exponential speedup is lost, but a polynomial quantum speedup is retained for sufficiently weak noise. In contrast to noise range, we find that breaking of spectral symmetry by the noise has no significant impact on the performance of the noisy algorithms. Our results about the long-range models highlight that care must be taken in selecting phenomenological noise models so as not to change the nature of the computational problem. We conclude from the short-range noise model results that the exponential speedup in the glued-trees problem is not robust to noise, but a polynomial quantum speedup is still possible.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover’s algorithm on the same device.

Active learning for noisy oracle via density power divergence

The accuracy of active learning is critically influenced by the existence of noisy labels given by a noisy oracle. In this paper, we propose a novel pool-based active learning framework through robust measures based on density power divergence. By minimizing density power divergence, such as β-divergence and γ-divergence, one can estimate the model accurately even under the existence of noisy labels within data. Accordingly, we develop query selecting measures for pool-based active learning using these divergences. In addition, we propose an evaluation scheme for these measures based on asymptotic statistical analyses, which enables us to perform active learning by evaluating an estimation error directly. Experiments with benchmark datasets and real-world image datasets show that our active learning scheme performs better than several baseline methods.

A probabilistic model of active learning with multiple noisy oracles

In this paper, we focus on obtaining an accurate classifier in active learning, when there are multiple noisy oracles with different and unknown levels of expertise to provide labels for selected instances. We propose a probabilistic model of active learning with multiple noisy oracles (PMActive). Our goal is formulized as to select the most reliable oracle and estimate the actual label on training data. When an instance is selected in every round of active learning, we firstly model the accuracies of individual oracles based on observed noisy labels, and select the most reliable oracle of all to provide a label for the instance. After adding the new instance-label pair into the training set, the actual label of the instance is estimated and used for enhancing the performance of the current classifier. The experimental results indicate that the PMActive method can work with different noise levels of oracles. Compared with the baselines which are commonly used in this area of active learning, the PMActive method is superior in obtaining a more accurate classifier.

Improved algorithms for quantum identification of Boolean oracles

The oracle identification problem (OIP) was introduced by Ambainis et al. [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS’04, in: LNCS, vol. 2996, 2004, pp. 105–116]. It is given as a set S of M oracles and a blackbox oracle f . Our task is to figure out which oracle in S is equal to the blackbox f by making queries to f . OIP includes several problems such as the Grover Search as special cases. In this paper, we improve the algorithms in [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS’04, in: LNCS, vol. 2996, 2004, pp. 105–116] by providing a mostly optimal upper bound of query complexity for this problem: (i) For any oracle set S such that | S | ≤ 2 N d ( d < 1 ) , we design an algorithm whose query complexity is O ( N log M / log N ) , matching the lower bound proved in [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS’04, in: LNCS, vol. 2996, 2004, pp. 105–116]. (ii) Our algorithm also works for the range between 2 N d and 2 N / log N (where the bound becomes O ( N ) ), but the gap between the upper and lower bounds worsens gradually. (iii) Our algorithm is robust, namely, it exhibits the same performance (up to a constant factor) against noisy oracles as also shown in the literature [M. Adcock, R. Cleve, A quantum Goldreich–Levin theorem with cryptographic applications, in: Proc. of STACS’02, in: LNCS, vol. 2285, 2002, pp. 323–334; H. Buhrman, I. Newman, H. Röhrig, R. deWolf, Robust quantum algorithms and polynomials, in: Proc. of STACS’05, in: LNCS, vol. 3404, 2005, pp. 593–604; P. Høyer, M. Mosca, R. de Wolf, Quantum search on bounded-error inputs, in: Proc. of ICALP’03, in: LNCS, vol. 2719, 2003, pp. 291–299] for special cases of OIP.

Effects of a random noisy oracle on search algorithm complexity

Grover's algorithm provides a quadratic speed-up over classical algorithms for unstructured database or library searches. This paper examines the robustness of Grover's search algorithm to a random phase error in the oracle and analyzes the complexity of the search process as a function of the scaling of the oracle error with database or library size. Both the discrete- and continuous-time implementations of the search algorithm are investigated. It is shown that unless the oracle phase error scales as O(N^(-1/4)), neither the discrete- nor the continuous-time implementation of Grover's algorithm is scalably robust to this error in the absence of error correction.

Multi-oracle interactive protocols with constant space verifiers

Multi-oracle interactive protocols are an extension of the Goldwasser-Micali-Rackof model, in which several infinitely powerful provers interact with a single resource-bounded verifier. In this paper we consider the language recognition power of such protocols and prove that a finite state verifier can accept any recursively enumerable set both in the multi-prover submodel of Ben-or, Goldwasser, Kilian, and Wigderson, and in the noisy oracle submodel of Feige, Shamir, and Tennenholtz. Unlike Lipton's single prover construction, our simulation of arbitrary Turing machine computations uses only polynomial overhead and stops with probability 1 (whenever the Turing machine stops). By using the new tehniques, we show that computing the expected payoff of reasonable games of incomplete information is undecidable, thus solving a long-standing open problem posed by Reif.