arXiv subjects

Bin Yu

Publications and source records attributed to Bin Yu.

At least 163 records · Page 9Linked to original sources

arXiv2019

A uniqueness theorem for transitive Anosov flows obtained by gluing hyperbolic plugs

In a previous paper with C. Bonatti ([5]), we have defined a general procedure to build new examples of Anosov flows in dimension 3. The procedure consists in gluing together some building blocks, called hyperbolic plugs, along their boundary in order to obtain a closed 3-manifold endowed with a complete flow. The main theorem of [5] states that (under some mild hypotheses) it is possible to choose the gluing maps so the resulting flow is Anosov. The aim of the present paper is to show a uniqueness result for Anosov flows obtained by such a procedure. Roughly speaking, we show that the orbital equivalence class of these Anosov flows is insensitive to the precise choice of the gluing maps used in the construction. The proof relies on a coding procedure which we find interesting for its own sake, and follows a strategy that was introduced by T. Barbot in a particular case.

math.DS↗

arXiv2019

Disentangled Attribution Curves for Interpreting Random Forests and Boosted Trees

Tree ensembles, such as random forests and AdaBoost, are ubiquitous machine learning models known for achieving strong predictive performance across a wide variety of domains. However, this strong performance comes at the cost of interpretability (i.e. users are unable to understand the relationships a trained random forest has learned and why it is making its predictions). In particular, it is challenging to understand how the contribution of a particular feature, or group of features, varies as their value changes. To address this, we introduce Disentangled Attribution Curves (DAC), a method to provide interpretations of tree ensemble methods in the form of (multivariate) feature importance curves. For a given variable, or group of variables, DAC plots the importance of a variable(s) as their value changes. We validate DAC on real data by showing that the curves can be used to increase the accuracy of logistic regression while maintaining interpretability, by including DAC as an additional feature. In simulation studies, DAC is shown to out-perform competing methods in the recovery of conditional expectations. Finally, through a case-study on the bike-sharing dataset, we demonstrate the use of DAC to uncover novel insights into a dataset.

stat.ML↗

arXiv2019

Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning

There is growing interest in estimating and analyzing heterogeneous treatment effects in experimental and observational studies. We describe a number of meta-algorithms that can take advantage of any supervised learning or regression method in machine learning and statistics to estimate the Conditional Average Treatment Effect (CATE) function. Meta-algorithms build on base algorithms---such as Random Forests (RF), Bayesian Additive Regression Trees (BART) or neural networks---to estimate the CATE, a function that the base algorithms are not designed to estimate directly. We introduce a new meta-algorithm, the X-learner, that is provably efficient when the number of units in one treatment group is much larger than in the other, and can exploit structural properties of the CATE function. For example, if the CATE function is linear and the response functions in treatment and control are Lipschitz continuous, the X-learner can still achieve the parametric rate under regularity conditions. We then introduce versions of the X-learner that use RF and BART as base learners. In extensive simulation studies, the X-learner performs favorably, although none of the meta-learners is uniformly the best. In two persuasion field experiments from political science, we demonstrate how our new X-learner can be used to target treatment regimes and to shed light on underlying mechanisms. A software package is provided that implements our methods.

math.ST↗

arXiv2019

Fast MCMC sampling algorithms on polytopes

We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods. The former is based on volumetric-logarithmic barrier introduced by Vaidya whereas the latter uses John's ellipsoids. We show that the Vaidya walk mixes in significantly fewer steps than the logarithmic-barrier based Dikin walk studied in past work. For a polytope in $\mathbb{R}^d$ defined by $n >d$ linear constraints, we show that the mixing time from a warm start is bounded as $\mathcal{O}(n^{0.5}d^{1.5})$, compared to the $\mathcal{O}(nd)$ mixing time bound for the Dikin walk. The cost of each step of the Vaidya walk is of the same order as the Dikin walk, and at most twice as large in terms of constant pre-factors. For the John walk, we prove an $\mathcal{O}(d^{2.5}\cdot\log^4(n/d))$ bound on its mixing time and conjecture that an improved variant of it could achieve a mixing time of $\mathcal{O}(d^2\cdot\text{polylog}(n/d))$. Additionally, we propose variants of the Vaidya and John walks that mix in polynomial time from a deterministic starting point. The speed-up of the Vaidya walk over the Dikin walk are illustrated in numerical examples.

stat.ML↗

arXiv2019

Unique Sharp Local Minimum in $\ell_1$-minimization Complete Dictionary Learning

We study the problem of globally recovering a dictionary from a set of signals via $\ell_1$-minimization. We assume that the signals are generated as i.i.d. random linear combinations of the $K$ atoms from a complete reference dictionary $D^*\in \mathbb R^{K\times K}$, where the linear combination coefficients are from either a Bernoulli type model or exact sparse model. First, we obtain a necessary and sufficient norm condition for the reference dictionary $D^*$ to be a sharp local minimum of the expected $\ell_1$ objective function. Our result substantially extends that of Wu and Yu (2015) and allows the combination coefficient to be non-negative. Secondly, we obtain an explicit bound on the region within which the objective value of the reference dictionary is minimal. Thirdly, we show that the reference dictionary is the unique sharp local minimum, thus establishing the first known global property of $\ell_1$-minimization dictionary learning. Motivated by the theoretical results, we introduce a perturbation-based test to determine whether a dictionary is a sharp local minimum of the objective function. In addition, we also propose a new dictionary learning algorithm based on Block Coordinate Descent, called DL-BCD, which is guaranteed to have monotonic convergence. Simulation studies show that DL-BCD has competitive performance in terms of recovery rate compared to many state-of-the-art dictionary learning algorithms.

stat.ML↗

arXiv2019

Hierarchical interpretations for neural network predictions

Deep neural networks (DNNs) have achieved impressive predictive performance due to their ability to learn complex, non-linear relationships between variables. However, the inability to effectively visualize these relationships has led to DNNs being characterized as black boxes and consequently limited their applications. To ameliorate this problem, we introduce the use of hierarchical interpretations to explain DNN predictions through our proposed method, agglomerative contextual decomposition (ACD). Given a prediction from a trained DNN, ACD produces a hierarchical clustering of the input features, along with the contribution of each cluster to the final prediction. This hierarchy is optimized to identify clusters of features that the DNN learned are predictive. Using examples from Stanford Sentiment Treebank and ImageNet, we show that ACD is effective at diagnosing incorrect predictions and identifying dataset bias. Through human experiments, we demonstrate that ACD enables users both to identify the more accurate of two DNNs and to better trust a DNN's outputs. We also find that ACD's hierarchy is largely robust to adversarial perturbations, implying that it captures fundamental aspects of the input and ignores spurious noise.

cs.LG↗

arXiv2019

Interpretable machine learning: definitions, methods, and applications

Machine-learning models have demonstrated great success in learning complex patterns that enable them to make predictions about unobserved data. In addition to using models for prediction, the ability to interpret what a model has learned is receiving an increasing amount of attention. However, this increased focus has led to considerable confusion about the notion of interpretability. In particular, it is unclear how the wide array of proposed interpretation methods are related, and what common concepts can be used to evaluate them. We aim to address these concerns by defining interpretability in the context of machine learning and introducing the Predictive, Descriptive, Relevant (PDR) framework for discussing interpretations. The PDR framework provides three overarching desiderata for evaluation: predictive accuracy, descriptive accuracy and relevancy, with relevancy judged relative to a human audience. Moreover, to help manage the deluge of interpretation methods, we introduce a categorization of existing techniques into model-based and post-hoc categories, with sub-groups including sparsity, modularity and simulatability. To demonstrate how practitioners can use the PDR framework to evaluate and understand interpretations, we provide numerous real-world examples. These examples highlight the often under-appreciated role played by human audiences in discussions of interpretability. Finally, based on our framework, we discuss limitations of existing methods and directions for future work. We hope that this work will provide a common vocabulary that will make it easier for both practitioners and researchers to discuss and choose from the full range of interpretation methods.

stat.ML↗

arXiv2018

An objective-adaptive refinement criterion based on modified ridge extraction method for finite-time Lyapunov exponent (FTLE) calculation

High-accuracy and high-efficiency finite-time Lyapunov exponent (FTLE) calculation method has long been a research hot point, and adaptive refinement method is a kind of method in this field. The proposed objective-adaptive refinement (OAR) criterion can put adaptive particles at the vicinity of FTLE ridges. The FTLE ridge is extracted not simply by the magnitude of FTLE (would cause false negative refinement) and error (would cause false positive refinement) but by a modified gradient climbing method. Moreover, the refinement regions converge to some certain region because of the objectivity of the refinement region.

physics.flu-dyn↗

arXiv2018

Mobile Robot Localisation and Navigation Using LEGO NXT and Ultrasonic Sensor

Mobile robots are becoming increasingly important both for individuals and industries. Mobile robotic technology is not only utilised by experts in this field but is also very popular among amateurs. However, implementing a mobile robot to perform tasks autonomously can be expensive because of the need for various types of sensors and the high price of robot platforms. Hence, in this paper we present a mobile robot localisation and navigation system which uses a LEGO ultrasonic sensor in an indoor map based on the LEGO MINDSTORM NXT. This provides an affordable and ready-to-use option for most robot fans. In this paper, an effective method is proposed to extract useful information from the distorted readings collected by the ultrasonic sensor. Then, the particle filter is used to localise the robot. After robot's position is estimated, a sampling-based path planning method is proposed for the robot navigation. This method reduces the robot accumulative motion error by minimising robot turning times and covering distances. The robot localisation and navigation algorithms are implemented in MATLAB. Simulation results show an average accuracy between 1 and 3 cm for three different indoor map locations. Furthermore, experiments performed in a real setup show the effectiveness of the proposed methods.

cs.RO↗

arXiv2018

High-speed Tracking with Multi-kernel Correlation Filters

Correlation filter (CF) based trackers are currently ranked top in terms of their performances. Nevertheless, only some of them, such as KCF~\cite{henriques15} and MKCF~\cite{tangm15}, are able to exploit the powerful discriminability of non-linear kernels. Although MKCF achieves more powerful discriminability than KCF through introducing multi-kernel learning (MKL) into KCF, its improvement over KCF is quite limited and its computational burden increases significantly in comparison with KCF. In this paper, we will introduce the MKL into KCF in a different way than MKCF. We reformulate the MKL version of CF objective function with its upper bound, alleviating the negative mutual interference of different kernels significantly. Our novel MKCF tracker, MKCFup, outperforms KCF and MKCF with large margins and can still work at very high fps. Extensive experiments on public datasets show that our method is superior to state-of-the-art algorithms for target objects of small move at very high speed.

cs.CV↗

arXiv2018

Beyond Word Importance: Contextual Decomposition to Extract Interactions from LSTMs

The driving force behind the recent success of LSTMs has been their ability to learn complex and non-linear relationships. Consequently, our inability to describe these relationships has led to LSTMs being characterized as black boxes. To this end, we introduce contextual decomposition (CD), an interpretation algorithm for analysing individual predictions made by standard LSTMs, without any changes to the underlying model. By decomposing the output of a LSTM, CD captures the contributions of combinations of words or variables to the final prediction of an LSTM. On the task of sentiment analysis with the Yelp and SST data sets, we show that CD is able to reliably identify words and phrases of contrasting sentiment, and how they are combined to yield the LSTM's final prediction. Using the phrase-level labels in SST, we also demonstrate that CD is able to successfully extract positive and negative negations from an LSTM, something which has not previously been done.

cs.CL↗

arXiv2018

Stability and Convergence Trade-off of Iterative Optimization Algorithms

The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly handled by algorithmic stability. The machine learning community has a rich history investigating convergence and stability separately. However, the question about the trade-off between these two quantities remains open. In this paper, we show that for any iterative algorithm at any iteration, the overall performance is lower bounded by the minimax statistical error over an appropriately chosen loss function class. This implies an important trade-off between convergence and stability of the algorithm -- a faster converging algorithm has to be less stable, and vice versa. As a direct consequence of this fundamental tradeoff, new convergence lower bounds can be derived for classes of algorithms constrained with different stability bounds. In particular, when the loss function is convex (or strongly convex) and smooth, we discuss the stability upper bounds of gradient descent (GD) and stochastic gradient descent and their variants with decreasing step sizes. For Nesterov's accelerated gradient descent (NAG) and heavy ball method (HB), we provide stability upper bounds for the quadratic loss function. Applying existing stability upper bounds for the gradient methods in our trade-off framework, we obtain lower bounds matching the well-established convergence upper bounds up to constants for these algorithms and conjecture similar lower bounds for NAG and HB. Finally, we numerically demonstrate the tightness of our stability bounds in terms of exponents in the rate and also illustrate via a simulated logistic regression problem that our stability bounds reflect the generalization errors better than the simple uniform convergence bounds for GD and NAG.

stat.ML↗

arXiv2018

Improved OpenCL-based Implementation of Social Field Pedestrian Model

Two aspects of improvements are proposed for the OpenCL-based implementation of the social field pedestrian model. In the aspect of algorithm, a method based on the idea of divide-and-conquer is devised in order to overcome the problem of global memory depletion when fields are of a larger size. This is of importance for the study of finer pedestrian walking behavior, which usually requires larger fields. In the aspect of computation, the OpenCL heterogeneous framework is thoroughly studied. Factors that may affect the numerical efficiency are evaluated, with regarding to the social field model previously proposed. This includes usage of local memory, deliberate patch of data structures for avoidance of bank conflicts, and so on. Numerical experiments disclose that the numerical efficiency is brought to an even higher level. Compared to the CPU model and the previous GPU model, the current GPU model can be at most 71.56 and 13.3 times faster respectively so that it is more qualified to be a core engine for analysis of super-large scale crowd.

cs.DC↗

arXiv2018

Towards the Standardization of Non-orthogonal Multiple Access for Next Generation Wireless Networks

Non-orthogonal multiple access (NoMA) as an efficient way of radio resource sharing can root back to the network information theory. For generations of wireless communication systems design, orthogonal multiple access (OMA) schemes in time, frequency, or code domain have been the main choices due to the limited processing capability in the transceiver hardware, as well as the modest traffic demands in both latency and connectivity. However, for the next generation radio systems, given its vision to connect everything and the much evolved hardware capability, NoMA has been identified as a promising technology to help achieve all the targets in system capacity, user connectivity, and service latency. This article will provide a systematic overview of the state-of-the-art design of the NoMA transmission based on a unified transceiver design framework, the related standardization progress, and some promising use cases in future cellular networks, based on which the interested researchers can get a quick start in this area.

cs.IT↗

arXiv2018

Solving Linear Programs with Complementarity Constraints using Branch-and-Cut

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium constraints. The presence of the complementarity constraints results in a nonconvex optimization problem. We develop a branch-and-cut algorithm to find a global optimum for this class of optimization problems, where we branch directly on complementarities. We develop branching rules and feasibility recovery procedures and demonstrate their computational effectiveness in a comparison with CPLEX. The implementation builds on CPLEX through the use of callback routines. The computational results show that our approach is a strong alternative to constructing an integer programming formulation using big-$M$ terms to represent bounds for variables, with testing conducted on general LPCCs as well as on instances generated from bilevel programs with convex quadratic lower level problems.

math.OC↗

arXiv2017

Iterative Random Forests to detect predictive and stable high-order interactions

Genomics has revolutionized biology, enabling the interrogation of whole transcriptomes, genome-wide binding sites for proteins, and many other molecular processes. However, individual genomic assays measure elements that interact in vivo as components of larger molecular machines. Understanding how these high-order interactions drive gene expression presents a substantial statistical challenge. Building on Random Forests (RF), Random Intersection Trees (RITs), and through extensive, biologically inspired simulations, we developed the iterative Random Forest algorithm (iRF). iRF trains a feature-weighted ensemble of decision trees to detect stable, high-order interactions with same order of computational cost as RF. We demonstrate the utility of iRF for high-order interaction discovery in two prediction problems: enhancer activity in the early Drosophila embryo and alternative splicing of primary transcripts in human derived cell lines. In Drosophila, among the 20 pairwise transcription factor interactions iRF identifies as stable (returned in more than half of bootstrap replicates), 80% have been previously reported as physical interactions. Moreover, novel third-order interactions, e.g. between Zelda (Zld), Giant (Gt), and Twist (Twi), suggest high-order relationships that are candidates for follow-up experiments. In human-derived cells, iRF re-discovered a central role of H3K36me3 in chromatin-mediated splicing regulation, and identified novel 5th and 6th order interactions, indicative of multi-valent nucleosomes with specific roles in splicing regulation. By decoupling the order of interactions from the computational cost of identification, iRF opens new avenues of inquiry into the molecular mechanisms underlying genome biology.

stat.ML↗

arXiv2017

Artificial Intelligence and Statistics

Artificial intelligence (AI) is intrinsically data-driven. It calls for the application of statistical concepts through human-machine collaboration during generation of data, development of algorithms, and evaluation of results. This paper discusses how such human-machine collaboration can be approached through the statistical concepts of population, question of interest, representativeness of training data, and scrutiny of results (PQRS). The PQRS workflow provides a conceptual framework for integrating statistical ideas with human input into AI products and research. These ideas include experimental design principles of randomization and local control as well as the principle of stability to gain reproducibility and interpretability of algorithms and data results. We discuss the use of these principles in the contexts of self-driving cars, automated medical diagnoses, and examples from the authors' collaborative research.

stat.ML↗

arXiv2017

Two-dimensional material based "field-effect CCD"

Charge-coupled device (CCD), along with the complementary metal-oxide-semiconductor (CMOS), is one of the major imaging technologies. Traditional CCDs rely on the charge transfer between potential wells, which gives them advantages of simple pixel structure, high sensitivity, and low noise. However, the serial transfer requires fabrication incompatible with CMOS, and leads to slower, more complex, and less flexible readout than random access. Here, we report a new-concept CCD called field-effect CCD (FE-CCD), which is based on the capacitive "coupling" between the semiconductor substrate and the 2D material. The strong field effect of the 2D material enables amplification, and non-destructive readout of the integrated charges in one pixel without transfer. We demonstrated the broadband response of our CCD (up to 1870 nm) and the successful integration of 2D hetero-structures for reducing the power consumption. The demonstrated FE-CCD provides a valuable strategy for versatile 2D materials to be monolithically integrated into the semiconductor imaging technology.

physics.app-ph↗