Probably Approximately Correct Research Articles

Clifford Circuits can be Properly PAC Learned if and only if RP=NP

Given a dataset of input states, measurements, and probabilities, is it possible to efficiently predict the measurement probabilities associated with a quantum circuit? Recent work of Caro and Datta \cite{2020Caro} studied the problem of PAC learning quantum circuits in an information theoretic sense, leaving open questions of computational efficiency. In particular, one candidate class of circuits for which an efficient learner might have been possible was that of Clifford circuits, since the corresponding set of states generated by such circuits, called stabilizer states, are known to be efficiently PAC learnable \cite{rocchetto2018stabiliser}. Here we provide a negative result, showing that proper learning of CNOT circuits with 1/ poly(n) error is hard for classical learners unless RP = NP, ruling out the possibility of strong learners under standard complexity theoretic assumptions. As the classical analogue and subset of Clifford circuits, this naturally leads to a hardness result for Clifford circuits as well. Additionally, we show that if RP = NP then there would exist efficient proper learning algorithms for CNOT and Clifford circuits. By similar arguments, we also find that an efficient proper quantum learner for such circuits exists if and only if NP ⊆ RQP. We leave open the problem of hardness for improper learning or O(1) error to future work.

Hypothesizing an algorithm from one example: the role of specificity.

Statistical machine learning usually achieves high-accuracy models by employing tens of thousands of examples. By contrast, both children and adult humans typically learn new concepts from either one or a small number of instances. The high data efficiency of human learning is not easily explained in terms of standard formal frameworks for machine learning, including Gold's learning-in-the-limit framework and Valiant's probably approximately correct (PAC) model. This paper explores ways in which this apparent disparity between human and machine learning can be reconciled by considering algorithms involving a preference for specificity combined with program minimality. It is shown how this can be efficiently enacted using hierarchical search based on identification of certificates and push-down automata to support hypothesizing compactly expressed maximal efficiency algorithms. Early results of a new system called DeepLog indicate that such approaches can support efficient top-down construction of relatively complex logic programs from a single example. This article is part of a discussion meeting issue 'Cognitive artificial intelligence'.

Effective Concept Classes of PAC and PACi Incomparable Degrees, Joins and Embedding of Degrees

AbstractThe Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: senadheerad@winthrop.eduURL: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864

Robust-PAC time-critical workflow offloading in edge-to-cloud continuum among heterogeneous resources

Edge-to-cloud continuum connects and extends the calculation from edge side via network to cloud platforms, where diverse workflows go back and forth, getting executed on scheduled calculation resources. To better utilize the calculation resources from all sides, workflow offloading problems have been investigating lately. Most works focus on optimizing constraints like: latency requirements, resource utilization rate limits, and energy consumption bounds. However, the dynamics among the offloading environment have hardly been researched, which easily results in uncertain Quality of Service(QoS) on the user side. Any part of the workload change, resource availability change or network latency could incur dynamics in an offloading environment. In this work, we propose a robust PAC (probably approximately correct) offloading algorithm to address this dynamic issue together with optimization. We train an LSTM-based sequence-to-sequence neural network to learn how to offload workflows in edge-to-cloud continuum. Comprehensive implementations and corresponding comparison against state-of-the-art methods demonstrate the robustness of our proposed algorithm. More specifically, our algorithm achieves better offloading performance regarding dynamic heterogeneous offloading environment and faster adaptation to newly changed environments than fine-tuned state-of-the-art RL-based offloading methods.

Kinematics Design of a MacPherson Suspension Architecture Based on Bayesian Optimization.

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months and is a significant cost in practice. We have developed a Bayesian optimization (BO) system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing the generalized inverse of a high-dimensional nonlinear function that does not require, for example, gradient information, which is often unavailable from discipline models. We furthermore develop a three-tier convergence criterion based on: 1) convergence to a solution optimally satisfying all specified design criteria; 2) detection that a design satisfying all criteria is infeasible; or 3) convergence to a probably approximately correct (PAC) solution. We demonstrate the proposed approach on benchmark functions and a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient and that the novel convergence criteria can be implemented straightforwardly based on the existing concepts and subroutines in popular BO software packages.

SEBD: A Stream Evolving Bot Detection Framework with Application of PAC Learning Approach to Maintain Accuracy and Confidence Levels

A simple supervised learning model can predict a class from trained data based on the previous learning process. Trust in such a model can be gained through evaluation measures that ensure fewer misclassification errors in prediction results for different classes. This can be applied to supervised learning using a well-trained dataset that covers different data points and has no imbalance issues. This task is challenging when it integrates a semi-supervised learning approach with a dynamic data stream, such as social network data. In this paper, we propose a stream-based evolving bot detection (SEBD) framework for Twitter that uses a deep graph neural network. Our SEBD framework was designed based on multi-view graph attention networks using fellowship links and profile features. It integrates Apache Kafka to enable the Twitter API stream and predict the account type after processing. We used a probably approximately correct (PAC) learning framework to evaluate SEBD’s results. Our objective was to maintain the accuracy and confidence levels of our framework to enable successful learning with low misclassification errors. We assessed our framework results via cross-domain evaluation using test holdout, machine learning classifiers, benchmark data, and a baseline tool. The overall results show that SEBD is able to successfully identify bot accounts in a stream-based manner. Using holdout and cross-validation with a random forest classifier, SEBD achieved an accuracy score of 0.97 and an AUC score of 0.98. Our results indicate that bot accounts participate highly in hashtags on Twitter.

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

Theoretical guarantee for crowdsourcing learning with unsure option

Crowdsourcing learning, in which labels are collected from multiple workers through crowdsourcing platforms, has attracted much attention during the past decade. This learning paradigm would reduce the labeling cost since crowdsourcing workers may be non-expert and hence less costly. On the other hand, crowdsourcing learning algorithms also suffer from being misled by incorrect labels introduced by imperfect workers. To control such risks, recently, it has been suggested to provide workers an additional unsure option during the labeling process. Although the benefits of the unsure option have been empirically demonstrated, theoretical analysis is still limited.In this article, a theoretical analysis of crowdsourcing learning with the unsure option is presented. Specifically, an upper bound of minimally sufficient number of crowd labels required for learning a probably approximately correct (PAC) classification model with and without the unsure option are given respectively. Next, a condition under which providing (or not providing) an unsure option to workers is derived. Then, the theoretical results are extended to guide non-identical label options (with or without unsure options) to different workers. Last, several useful applications are proposed based on theoretical results.

Semi-Supervised Heterogeneous Domain Adaptation: Theory and Algorithms.

Semi-supervised heterogeneous domain adaptation (SsHeDA) aims to train a classifier for the target domain, in which only unlabeled and a small number of labeled data are available. This is done by leveraging knowledge acquired from a heterogeneous source domain. From algorithmic perspectives, several methods have been proposed to solve the SsHeDA problem; yet there is still no theoretical foundation to explain the nature of the SsHeDA problem or to guide new and better solutions. Motivated by compatibility condition in semi-supervised probably approximately correct (PAC) theory, we explain the SsHeDA problem by proving its generalization error - that is, why labeled heterogeneous source data and unlabeled target data help to reduce the target risk. Guided by our theory, we devise two algorithms as proof of concept. One, kernel heterogeneous domain alignment (KHDA), is a kernel-based algorithm; the other, joint mean embedding alignment (JMEA), is a neural network-based algorithm. When a dataset is small, KHDA's training time is less than JMEA's. When a dataset is large, JMEA is more accurate in the target domain. Comprehensive experiments with image/text classification tasks show KHDA to be the most accurate among all non-neural network baselines, and JMEA to be the most accurate among all baselines.

Data-Driven Abstractions With Probabilistic Guarantees for Linear PETC Systems

We employ the scenario approach to compute probably approximately correct (PAC) bounds on the average inter-sample time (AIST) generated by an unknown PETC system, based on a finite number of samples. We extend the scenario optimisation to multiclass SVM algorithms in order to construct a PAC map between the concrete state-space and the inter-sample times. We then build a traffic model applying an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $ </tex-math></inline-formula> -complete relation and find, in the underlying graph, the cycles of minimum and maximum average weight: these provide lower and upper bounds on the AIST. Numerical benchmarks show the practical applicability of our method, which is compared against model-based state-of-the-art tools.

An Evaluation Method of the Anti-Modeling-Attack Capability of PUFs

The physical unclonable function (PUF) is regarded as the root of trust of hardware systems. However, it suffers from the modeling attacks based on machine learning (ML) algorithms. Subsequently, the anti-modeling-attack PUF is of great concern from academia and industries in recent years. In practice, the security of a given PUF is evaluated after the pertinent attacks. However, these evaluation methods are not helpful for the PUF design, because the relationship between the PUF structure and the anti-modeling-attack capability is not established explicitly. This work proposes a security evaluation method of PUF based on the mimic attack and the Probably Approximately Correct (PAC) theory. The anti-modeling-attack capability of PUF is measured by the corresponding area enclosed by the evaluation curve. Twenty representative types of PUFs with different sizes are evaluated by the proposed method. It shows that the proposed method is effective, because the evaluation results are consistent with the difficulties of modeling attacks for the corresponding PUFs in the design practices. And the evaluation results are able to assist the PUF design.

Learning Hidden Graphs from Samples.

Several real-world problems, like molecular biology and chemical reactions, have hidden graphs, and we need to learn the hidden graph using edge-detecting samples. In this problem, the learner receives examples explaining whether a set of vertices induces an edge of the hidden graph. This paper examines the learnability of this problem using the PAC and Agnostic PAC learning models. By computing the VC-dimension of hypothesis spaces of hidden graphs, hidden trees, hidden connected graphs, and hidden planar graphs through edge-detecting samples, we also find the sample complexity of learning these spaces. We study the learnability of this space of hidden graphs in two cases, namely for known and unknown vertex sets. We show that the class of hidden graphs is uniformly learnable when the vertex set is known. Furthermore, we prove that the family of hidden graphs is not uniformly learnable but is nonuniformly learnable when the vertex set is unknown.

A semisupervised classification algorithm combining noise learning theory and a disagreement cotraining framework

In the era of big data, the data in many business scenarios are characterized by a small number of labelled samples and a large number of unlabelled samples. It is quite difficult to classify and identify such data and provide effective decision support for a business. A commonly employed processing method in this kind of data scenario is the disagreement-based semisupervised learning method, i.e., exchanging high-confidence samples among multiple models as pseudolabel samples to improve each model’s classification performance. As such pseudolabel samples inevitably contain label noise, they may interfere with the subsequent model learning and damage the robustness of the ensemble model. To solve this problem, a semisupervised classification algorithm based on noise learning theory and a disagreement cotraining framework is proposed. In this model, first, the probably approximately correct (PAC) estimation theory under label noise conditions is applied, the relationship between the label noise level and model robust estimation in the process of multiround cotraining is discussed, and a disagreement elimination algorithm framework based on multiple-model (feature argument and select (FANS) algorithm and L1 penalized logistics regression (PLR) algorithm) cotraining is constructed based on this theoretical relationship. The experimental results show that the algorithm proposed in this paper gives not only a high-confidence sample set that meets the upper bound constraint of the label noise level but also a robust ensemble model capable of resisting sampling bias. The work performed in this paper provides a new research perspective for semisupervised learning theory based on disagreement.

Identification of immune-related genes and development of a prognostic model in mantle cell lymphoma.

The immune landscape, prognostic model, and molecular variations of mantle cell lymphoma (MCL) remain unclear. Hence, an integrated bioinformatics analysis of MCL datasets is required for the development of immunotherapy and the optimization of targeted therapies. Data were obtained from the Gene Expression Omnibus (GEO) database (GSE32018, GSE45717 and GSE93291). The differentially expressed immune-related genes were selected, and the hub genes were screened by three machine learning algorithms, followed by enrichment and correlation analyses. Next, MCL molecular clusters based on the hub genes were identified by K-Means clustering, the probably approximately correct (PAC) algorithm, and principal component analysis (PCA). The landscape of immune cell infiltration and immune checkpoint molecules in distinct clusters was explored by single-sample gene-set enrichment analysis (ssGSEA) as well as the CIBERSORT and xCell algorithms. The prognostic genes and prognostic risk score model for MCL clusters were identified by least absolute shrinkage and selection operator (LASSO)-Cox analysis and cross-validation for lambda. Correlation analysis was performed to explore the correlation between the screened prognostic genes and immune cells or immune checkpoint molecules. Four immune-related hub genes (CD247, CD3E, CD4, and GATA3) were screened in MCL, mainly enriched in the T-cell receptor signaling pathway. Based on the hub genes, two MCL molecular clusters were recognized. The cluster 2 group had a significantly worse overall survival (OS), with down-regulated hub genes, and a variety of activated immune effector cells declined. The majority of immune checkpoint molecules had also decreased. An efficient prognostic model was established, including six prognostic genes (LGALS2, LAMP3, ICOS, FCAMR, IGFBP4, and C1QA) differentially expressed between two MCL clusters. Patients with a higher risk score in the prognostic model had a poor prognosis. Furthermore, most types of immune cells and a range of immune checkpoint molecules were positively correlated with the prognostic genes. Our study identified distinct molecular clusters based on the immune-related hub genes, and showed that the prognostic model affected the prognosis of MCL patients. These hub genes, modulated immune cells, and immune checkpoint molecules might be involved in oncogenesis and could be potential prognostic biomarkers in MCL.

ENSIGHTS: Intelligent Monitoring of Electric Power Transmission Assets

This work aims to use Data Science techniques to build predictive models that will eventually improve maintenance plans regarding power transformers by reducing shutoffs and transmission downtime. This work is part of a 36-month long Research and Development (R&amp;D) project started on January 2021, as of the writing of this report the project is halfway through. The analytic models described herein have already been tested while most of the remaining work is yet to be done. In a single Data Lake environment, we will consolidate several databases from information systems that support the company's operation and maintenance processes. Various machine learning models will run on this data, and their results will appear in a dashboard, alongside several traditional indicators. This process will be integrated and consolidated in a computing platform with cloud architecture. We use Machine Learning (ML) to develop the models. Based on an Agnostic Probably Approximately Correct (PAC) Learning study of the available datasets estimating their Vapnik–Chervonenkis dimension, we choose Random Forests (RF) algorithms to be used in the new indicators. So far, the project has produced two new indicators: Chromatographic Assay Indicator (CAI) and Electrical Failure Risk Indicator (EFRI). The CAI indicator evaluation uses a Random Forest Algorithm trained with an external dataset due to the small number of power transformers failures in the O&amp;M data. This indicator performed much better than classical chromatographic indicators to predict electric or temperature problems on the test set. The EFRI indicator correlates monitoring data available from an existing Supervisory Control and Data Acquisition (SCADA) system with maintenance data from an existing Enterprise Resource Planning (ERP) system through a RF algorithm capable of alerting to a higher risk of electric failure. ANEEL funds this work as R&amp;D project PD-00394-1907/2019 titled “Aplicabilidade de nova tecnologia voltada para o desenvolvimento de um modelo de monitoramento inteligente dos ativos de transmissão”.

ENSIGHTS: Intelligent Monitoring of Electric Power Transmission Assets

This work aims to use Data Science techniques to build predictive models that will eventually improve maintenance plans regarding power transformers by reducing shutoffs and transmission downtime. This work is part of a 36-month long Research and Development (R&amp;D) project started on January 2021, as of the writing of this report the project is halfway through. The analytic models described herein have already been tested while most of the remaining work is yet to be done. In a single Data Lake environment, we will consolidate several databases from information systems that support the company's operation and maintenance processes. Various machine learning models will run on this data, and their results will appear in a dashboard, alongside several traditional indicators. This process will be integrated and consolidated in a computing platform with cloud architecture. We use Machine Learning (ML) to develop the models. Based on an Agnostic Probably Approximately Correct (PAC) Learning study of the available datasets estimating their Vapnik–Chervonenkis dimension, we choose Random Forests (RF) algorithms to be used in the new indicators. So far, the project has produced two new indicators: Chromatographic Assay Indicator (CAI) and Electrical Failure Risk Indicator (EFRI). The CAI indicator evaluation uses a Random Forest Algorithm trained with an external dataset due to the small number of power transformers failures in the O&amp;M data. This indicator performed much better than classical chromatographic indicators to predict electric or temperature problems on the test set. The EFRI indicator correlates monitoring data available from an existing Supervisory Control and Data Acquisition (SCADA) system with maintenance data from an existing Enterprise Resource Planning (ERP) system through a RF algorithm capable of alerting to a higher risk of electric failure. ANEEL funds this work as R&amp;D project PD-00394-1907/2019 titled “Aplicabilidade de nova tecnologia voltada para o desenvolvimento de um modelo de monitoramento inteligente dos ativos de transmissão”.

Sim-to-Lab-to-Real: Safe reinforcement learning with shielding and generalization guarantees

Safety is a critical component of autonomous systems and remains a challenge for learning-based policies to be utilized in the real world. In particular, policies learned using reinforcement learning often fail to generalize to novel environments due to unsafe behavior. In this paper, we propose Sim-to-Lab-to-Real to bridge the reality gap with a probabilistically guaranteed safety-aware policy distribution. To improve safety, we apply a dual policy setup where a performance policy is trained using the cumulative task reward and a backup (safety) policy is trained by solving the Safety Bellman Equation based on Hamilton-Jacobi (HJ) reachability analysis. In Sim-to-Lab transfer, we apply a supervisory control scheme to shield unsafe actions during exploration; in Lab-to-Real transfer, we leverage the Probably Approximately Correct (PAC)-Bayes framework to provide lower bounds on the expected performance and safety of policies in unseen environments. Additionally, inheriting from the HJ reachability analysis, the bound accounts for the expectation over the worst-case safety in each environment. We empirically study the proposed framework for ego-vision navigation in two types of indoor environments with varying degrees of photorealism. We also demonstrate strong generalization performance through hardware experiments in real indoor spaces with a quadrupedal robot. See https://sites.google.com/princeton.edu/sim-to-lab-to-real for supplementary material.

Probably Approximately Correct Learning in Adversarial Environments With Temporal Logic Specifications

Reinforcement learning (RL) algorithms have been used to learn how to implement tasks in uncertain and partially unknown environments. In practice, environments are usually uncontrolled and may affect task performance in an adversarial way. In this article, we model the interaction between an RL agent and its potentially adversarial environment as a turn-based zero-sum stochastic game. The task requirements are represented both qualitatively as a subset of linear temporal logic (LTL) specifications, and quantitatively as a reward function. For each case in which the LTL specification is realizable and can be equivalently transformed into a deterministic Büchi automaton, we show that there always exists a memoryless almost-sure winning strategy that is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -optimal for the discounted-sum objective for any arbitrary positive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> . We propose a probably approximately correct (PAC) learning algorithm that learns such a strategy efficiently in an online manner with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> unknown reward functions and unknown transition distributions. To the best of our knowledge, this is the first result on PAC learning in stochastic games with independent quantitative and qualitative objectives.

Private and Online Learnability Are Equivalent

Let H be a binary-labeled concept class. We prove that H can be PAC learned by an (approximate) differentially private algorithm if and only if it has a finite Littlestone dimension. This implies a qualitative equivalence between online learnability and private PAC learnability.

Differentially Private Learning of Geometric Concepts

We present differentially private efficient algorithms for learning union of polygons in the plane (which are not necessarily convex). Our algorithms achieve $(\alpha,\beta)$-PAC learning and $(\epsilon,\delta)$-differential privacy using a sample of size $\tilde{O}\left(\frac{1}{\alpha\epsilon}k\log d\right)$, where the domain is $[d]\times[d]$ and $k$ is the number of edges in the union of polygons.