Random forests are a combination of tree predictors such that each tree depends on the values of a random vector sampled independently and with the same distribution for all trees in the forest. The generalization error for forests converges a.s. to a limit as the number of trees in the forest becomes large. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation between them. Using a random selection of features to split each node yields error rates that compare favorably to Adaboost (Y. Freund & R. Schapire, Machine Learning: Proceedings of the Thirteenth International conference, aaa, 148–156), but are more robust with respect to noise. Internal estimates monitor error, strength, and correlation and these are used to show the response to increasing the number of features used in the splitting. Internal estimates are also used to measure variable importance. These ideas are also applicable to regression.

Random Forests

Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Deep Learning

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Numerical Optimization

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class. These theorems result in a geometric interpretation of what it means for an algorithm to be well suited to an optimization problem. Applications of the NFL theorems to information-theoretic aspects of optimization and benchmark measures of performance are also presented. Other issues addressed include time-varying optimization problems and a priori "head-to-head" minimax distinctions between optimization algorithms, distinctions that result despite the NFL theorems' enforcing of a type of uniformity over all algorithms.

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No free lunch theorems for optimization

Domain shift is unavoidable in real-world applications of object detection. For example, in self-driving cars, the target domain consists of unconstrained road environments which cannot all possibly be observed in training data. Similarly, in surveillance applications sufficiently representative training data may be lacking due to privacy regulations. In this paper, we address the domain adaptation problem from the perspective of robust learning and show that the problem may be formulated as training with noisy labels. We propose a robust object detection framework that is resilient to noise in bounding box class labels, locations and size annotations. To adapt to the domain shift, the model is trained on the target domain using a set of noisy object bounding boxes that are obtained by a detection model trained only in the source domain. We evaluate the accuracy of our approach in various source/target domain pairs and demonstrate that the model significantly improves the state-of-the-art on multiple domain adaptation scenarios on the SIM10K, Cityscapes and KITTI datasets.

/pdf/a-robust-learning-approach-to-domain-adaptive-object-wysomsqrs4.pdf

A Robust Learning Approach to Domain Adaptive Object Detection

Bagging (Breiman, 1994a) is a technique that tries to improve a learning algorithm‘s performance by using bootstrap replicates of the training set (Efron & Tibshirani, 1993, Efron, 1979). The computational requirements for estimating the resultant generalization error on a test set by means of cross-validation are often prohibitive, for leave-one-out cross-validation one needs to train the underlying algorithm on the order of mν times, where m is the size of the training set and ν is the number of replicates. This paper presents several techniques for estimating the generalization error of a bagged learning algorithm without invoking yet more training of the underlying learning algorithm (beyond that of the bagging itself), as is required by cross-validation-based estimation. These techniques all exploit the bias-variance decomposition (Geman, Bienenstock & Doursat, 1992, Wolpert, 1996). The best of our estimators also exploits stacking (Wolpert, 1992). In a set of experiments reported here, it was found to be more accurate than both the alternative cross-validation-based estimator of the bagged algorithm‘s error and the cross-validation-based estimator of the underlying algorithm‘s error. This improvement was particularly pronounced for small test sets. This suggests a novel justification for using bagging—more accurate estimation of the generalization error than is possible without bagging.

/pdf/an-efficient-method-to-estimate-bagging-s-generalization-3vkn8vru2k.pdf

An Efficient Method To Estimate Bagging‘s Generalization Error

Technological evolution and adaptive organizations: Ideas from biology may find applications in economics

This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.

/pdf/discrete-optimization-using-quantum-annealing-on-sparse-2s4ln8iaq5.pdf

Discrete optimization using quantum annealing on sparse Ising models

We explore the two-armed bandit with Gaussian payoffs as a theoretical model for optimization. The problem is formulated from a Bayesian perspective, and the optimal strategy for both one and two pulls is provided. We present regions of parameter space where a greedy strategy is provably optimal. We also compare the greedy and optimal strategies to one based on a genetic algorithm. In doing so, we correct a previous error in the literature concerning the Gaussian bandit problem and the supposed optimality of genetic algorithms for this problem. Finally, we provide an analytically simple bandit model that is more directly applicable to optimization theory than the traditional bandit problem and determine a near-optimal strategy for that model.

William G. Macready

Papers

A Robust Learning Approach to Domain Adaptive Object Detection

An Efficient Method To Estimate Bagging‘s Generalization Error

Technological evolution and adaptive organizations: Ideas from biology may find applications in economics

Discrete optimization using quantum annealing on sparse Ising models

Bandit problems and the exploration/exploitation tradeoff