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A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only valid under special assumptions of measurability of the class, in which case the PAC learnability even becomes consistent. Otherwise, there is a classical example, constructed under the Continuum Hypothesis by Dudley and Durst and further adapted by Blumer, Ehrenfeucht, Haussler, and Warmuth, of a concept class of VC dimension one which is neither uniform Glivenko-Cantelli nor consistently PAC learnable. We show that, rather surprisingly, under an additional set-theoretic hypothesis which is much milder than the Continuum Hypothesis (Martin's Axiom), PAC learnability is equivalent to finite VC dimension for every concept class.
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PAC learnability versus VC dimension: a footnote to a basic result of
statistical learning
| 2,200
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Q-learning is a reliable but inefficient off-policy temporal-difference method, backing up reward only one step at a time. Replacing traces, using a recency heuristic, are more efficient but less reliable. In this work, we introduce model-free, off-policy temporal difference methods that make better use of experience than Watkins' Q(\lambda). We introduce both Optimistic Q(\lambda) and the temporal second difference trace (TSDT). TSDT is particularly powerful in deterministic domains. TSDT uses neither recency nor frequency heuristics, storing (s,a,r,s',\delta) so that off-policy updates can be performed after apparently suboptimal actions have been taken. There are additional advantages when using state abstraction, as in MAXQ. We demonstrate that TSDT does significantly better than both Q-learning and Watkins' Q(\lambda) in a deterministic cliff-walking domain. Results in a noisy cliff-walking domain are less advantageous for TSDT, but demonstrate the efficacy of Optimistic Q(\lambda), a replacing trace with some of the advantages of TSDT.
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Temporal Second Difference Traces
| 2,201
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In experimenting with off-policy temporal difference (TD) methods in hierarchical reinforcement learning (HRL) systems, we have observed unwanted on-policy learning under reproducible conditions. Here we present modifications to several TD methods that prevent unintentional on-policy learning from occurring. These modifications create a tension between exploration and learning. Traditional TD methods require commitment to finishing subtasks without exploration in order to update Q-values for early actions with high probability. One-step intra-option learning and temporal second difference traces (TSDT) do not suffer from this limitation. We demonstrate that our HRL system is efficient without commitment to completion of subtasks in a cliff-walking domain, contrary to a widespread claim in the literature that it is critical for efficiency of learning. Furthermore, decreasing commitment as exploration progresses is shown to improve both online performance and the resultant policy in the taxicab domain, opening a new avenue for research into when it is more beneficial to continue with the current subtask or to replan.
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Reducing Commitment to Tasks with Off-Policy Hierarchical Reinforcement
Learning
| 2,202
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In this paper we present methods for attacking and defending $k$-gram statistical analysis techniques that are used, for example, in network traffic analysis and covert channel detection. The main new result is our demonstration of how to use a behavior's or process' $k$-order statistics to build a stochastic process that has those same $k$-order stationary statistics but possesses different, deliberately designed, $(k+1)$-order statistics if desired. Such a model realizes a "complexification" of the process or behavior which a defender can use to monitor whether an attacker is shaping the behavior. By deliberately introducing designed $(k+1)$-order behaviors, the defender can check to see if those behaviors are present in the data. We also develop constructs for source codes that respect the $k$-order statistics of a process while encoding covert information. One fundamental consequence of these results is that certain types of behavior analyses techniques come down to an {\em arms race} in the sense that the advantage goes to the party that has more computing resources applied to the problem.
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Attacking and Defending Covert Channels and Behavioral Models
| 2,203
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We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions provided by this algorithm are very accurate and they satisfy the optimality conditions more strictly than other SVM optimization algorithms. In many machine learning application, however, this strict optimality is often unnecessary, and it adversely affects the computational efficiency. Our algorithm can generate the path of suboptimal solutions within an arbitrary user-specified tolerance level. It allows us to control the trade-off between the accuracy of the solution and the computational cost. Moreover, We also show that our suboptimal solutions can be interpreted as the solution of a \emph{perturbed optimization problem} from the original one. We provide some theoretical analyses of our algorithm based on this novel interpretation. The experimental results also demonstrate the effectiveness of our algorithm.
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Suboptimal Solution Path Algorithm for Support Vector Machine
| 2,204
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We study the prevalent problem when a test distribution differs from the training distribution. We consider a setting where our training set consists of a small number of sample domains, but where we have many samples in each domain. Our goal is to generalize to a new domain. For example, we may want to learn a similarity function using only certain classes of objects, but we desire that this similarity function be applicable to object classes not present in our training sample (e.g. we might seek to learn that "dogs are similar to dogs" even though images of dogs were absent from our training set). Our theoretical analysis shows that we can select many more features than domains while avoiding overfitting by utilizing data-dependent variance properties. We present a greedy feature selection algorithm based on using T-statistics. Our experiments validate this theory showing that our T-statistic based greedy feature selection is more robust at avoiding overfitting than the classical greedy procedure.
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Domain Adaptation: Overfitting and Small Sample Statistics
| 2,205
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We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form "is object 'a' more similar to 'b' or to 'c'?" and is chosen to be maximally informative given the preceding responses. The output is an embedding of the objects into Euclidean space (like MDS); we refer to this as the "crowd kernel." SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as "is striped" among neckties and "vowel vs. consonant" among letters.
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Adaptively Learning the Crowd Kernel
| 2,206
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In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>) \le\exp<(-\frac{1}{N^2}\sum_{i=1}^{N}\frac{\epsilon^{2}}{2\sigma_{i}^{2}}>), \] where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random variables and $\sigma_i$ is the variance of the $i$th random variable.
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A Maximal Large Deviation Inequality for Sub-Gaussian Variables
| 2,207
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We provide a natural learning process in which a financial trader without a risk receives a gain in case when Stock Market is inefficient. In this process, the trader rationally choose his gambles using a prediction made by a randomized calibrated algorithm. Our strategy is based on Dawid's notion of calibration with more general changing checking rules and on some modification of Kakade and Foster's randomized algorithm for computing calibrated forecasts.
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Calibration with Changing Checking Rules and Its Application to
Short-Term Trading
| 2,208
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We begin this report by describing the Probably Approximately Correct (PAC) model for learning a concept class, consisting of subsets of a domain, and a function class, consisting of functions from the domain to the unit interval. Two combinatorial parameters, the Vapnik-Chervonenkis (VC) dimension and its generalization, the Fat Shattering dimension of scale e, are explained and a few examples of their calculations are given with proofs. We then explain Sauer's Lemma, which involves the VC dimension and is used to prove the equivalence of a concept class being distribution-free PAC learnable and it having finite VC dimension. As the main new result of our research, we explore the construction of a new function class, obtained by forming compositions with a continuous logic connective, a uniformly continuous function from the unit hypercube to the unit interval, from a collection of function classes. Vidyasagar had proved that such a composition function class has finite Fat Shattering dimension of all scales if the classes in the original collection do; however, no estimates of the dimension were known. Using results by Mendelson-Vershynin and Talagrand, we bound the Fat Shattering dimension of scale e of this new function class in terms of the Fat Shattering dimensions of the collection's classes. We conclude this report by providing a few open questions and future research topics involving the PAC learning model.
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Bounding the Fat Shattering Dimension of a Composition Function Class
Built Using a Continuous Logic Connective
| 2,209
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In batch learning, stability together with existence and uniqueness of the solution corresponds to well-posedness of Empirical Risk Minimization (ERM) methods; recently, it was proved that CV_loo stability is necessary and sufficient for generalization and consistency of ERM. In this note, we introduce CV_on stability, which plays a similar note in online learning. We show that stochastic gradient descent (SDG) with the usual hypotheses is CVon stable and we then discuss the implications of CV_on stability for convergence of SGD.
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Online Learning, Stability, and Stochastic Gradient Descent
| 2,210
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Music prediction tasks range from predicting tags given a song or clip of audio, predicting the name of the artist, or predicting related songs given a song, clip, artist name or tag. That is, we are interested in every semantic relationship between the different musical concepts in our database. In realistically sized databases, the number of songs is measured in the hundreds of thousands or more, and the number of artists in the tens of thousands or more, providing a considerable challenge to standard machine learning techniques. In this work, we propose a method that scales to such datasets which attempts to capture the semantic similarities between the database items by modeling audio, artist names, and tags in a single low-dimensional semantic space. This choice of space is learnt by optimizing the set of prediction tasks of interest jointly using multi-task learning. Our method both outperforms baseline methods and, in comparison to them, is faster and consumes less memory. We then demonstrate how our method learns an interpretable model, where the semantic space captures well the similarities of interest.
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Large-Scale Music Annotation and Retrieval: Learning to Rank in Joint
Semantic Spaces
| 2,211
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We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results.
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Kernel Belief Propagation
| 2,212
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The classical perceptron rule provides a varying upper bound on the maximum margin, namely the length of the current weight vector divided by the total number of updates up to that time. Requiring that the perceptron updates its internal state whenever the normalized margin of a pattern is found not to exceed a certain fraction of this dynamic upper bound we construct a new approximate maximum margin classifier called the perceptron with dynamic margin (PDM). We demonstrate that PDM converges in a finite number of steps and derive an upper bound on them. We also compare experimentally PDM with other perceptron-like algorithms and support vector machines on hard margin tasks involving linear kernels which are equivalent to 2-norm soft margin.
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The Perceptron with Dynamic Margin
| 2,213
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Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to approximate a set $P$ of $n$ elements (say, points) by a shape $x$ from a (possibly infinite) family $X$ of shapes. Here, each point $p\in P$ corresponds to a function $f$ such that $f(x)$ is the distance from $p$ to $x$, and we seek a shape $x$ that minimizes the sum of distances from each point in $P$. In the $k$-clustering variant, each $x\in X$ is a tuple of $k$ shapes, and $f(x)$ is the distance from $p$ to its closest shape in $x$. Our main result is a unified framework for constructing {\em coresets} and {\em approximate clustering} for such general sets of functions. To achieve our results, we forge a link between the classic and well defined notion of $\varepsilon$-approximations from the theory of PAC Learning and VC dimension, to the relatively new (and not so consistent) paradigm of coresets, which are some kind of "compressed representation" of the input set $F$. Using traditional techniques, a coreset usually implies an LTAS (linear time approximation scheme) for the corresponding optimization problem, which can be computed in parallel, via one pass over the data, and using only polylogarithmic space (i.e, in the streaming model). We show how to generalize the results of our framework for squared distances (as in $k$-mean), distances to the $q$th power, and deterministic constructions.
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A Unified Framework for Approximating and Clustering Data
| 2,214
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The main principle of stacked generalization (or Stacking) is using a second-level generalizer to combine the outputs of base classifiers in an ensemble. In this paper, we investigate different combination types under the stacking framework; namely weighted sum (WS), class-dependent weighted sum (CWS) and linear stacked generalization (LSG). For learning the weights, we propose using regularized empirical risk minimization with the hinge loss. In addition, we propose using group sparsity for regularization to facilitate classifier selection. We performed experiments using two different ensemble setups with differing diversities on 8 real-world datasets. Results show the power of regularized learning with the hinge loss function. Using sparse regularization, we are able to reduce the number of selected classifiers of the diverse ensemble without sacrificing accuracy. With the non-diverse ensembles, we even gain accuracy on average by using sparse regularization.
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Max-Margin Stacking and Sparse Regularization for Linear Classifier
Combination and Selection
| 2,215
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This paper introduces a machine learning based collaborative multi-band spectrum sensing policy for cognitive radios. The proposed sensing policy guides secondary users to focus the search of unused radio spectrum to those frequencies that persistently provide them high data rate. The proposed policy is based on machine learning, which makes it adaptive with the temporally and spatially varying radio spectrum. Furthermore, there is no need for dynamic modeling of the primary activity since it is implicitly learned over time. Energy efficiency is achieved by minimizing the number of assigned sensors per each subband under a constraint on miss detection probability. It is important to control the missed detections because they cause collisions with primary transmissions and lead to retransmissions at both the primary and secondary user. Simulations show that the proposed machine learning based sensing policy improves the overall throughput of the secondary network and improves the energy efficiency while controlling the miss detection probability.
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Reinforcement learning based sensing policy optimization for energy
efficient cognitive radio networks
| 2,216
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This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some variables, and never observe other variables; from this, we would like to find the dependency structure between the observed variables - separating out the spurious interactions caused by the (marginalizing out of the) latent variables' time series. We develop a new method, based on convex optimization, to do so in the case when the number of latent variables is smaller than the number of observed ones. For the case when the dependency structure between the observed variables is sparse, we theoretically establish a high-dimensional scaling result for structure recovery. We verify our theoretical result with both synthetic and real data (from the stock market).
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Learning the Dependence Graph of Time Series with Latent Factors
| 2,217
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Estimator algorithms in learning automata are useful tools for adaptive, real-time optimization in computer science and engineering applications. This paper investigates theoretical convergence properties for a special case of estimator algorithms: the pursuit learning algorithm. In this note, we identify and fill a gap in existing proofs of probabilistic convergence for pursuit learning. It is tradition to take the pursuit learning tuning parameter to be fixed in practical applications, but our proof sheds light on the importance of a vanishing sequence of tuning parameters in a theoretical convergence analysis.
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On epsilon-optimality of the pursuit learning algorithm
| 2,218
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One of the major challenges of ECoG-based Brain-Machine Interfaces is the movement prediction of a human subject. Several methods exist to predict an arm 2-D trajectory. The fourth BCI Competition gives a dataset in which the aim is to predict individual finger movements (5-D trajectory). The difficulty lies in the fact that there is no simple relation between ECoG signals and finger movement. We propose in this paper to decode finger flexions using switching models. This method permits to simplify the system as it is now described as an ensemble of linear models depending on an internal state. We show that an interesting accuracy prediction can be obtained by such a model.
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Decoding finger movements from ECoG signals using switching linear
models
| 2,219
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Signal Sequence Labeling consists in predicting a sequence of labels given an observed sequence of samples. A naive way is to filter the signal in order to reduce the noise and to apply a classification algorithm on the filtered samples. We propose in this paper to jointly learn the filter with the classifier leading to a large margin filtering for classification. This method allows to learn the optimal cutoff frequency and phase of the filter that may be different from zero. Two methods are proposed and tested on a toy dataset and on a real life BCI dataset from BCI Competition III.
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Large margin filtering for signal sequence labeling
| 2,220
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This paper addresses the pattern classification problem arising when available target data include some uncertainty information. Target data considered here is either qualitative (a class label) or quantitative (an estimation of the posterior probability). Our main contribution is a SVM inspired formulation of this problem allowing to take into account class label through a hinge loss as well as probability estimates using epsilon-insensitive cost function together with a minimum norm (maximum margin) objective. This formulation shows a dual form leading to a quadratic problem and allows the use of a representer theorem and associated kernel. The solution provided can be used for both decision and posterior probability estimation. Based on empirical evidence our method outperforms regular SVM in terms of probability predictions and classification performances.
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Handling uncertainties in SVM classification
| 2,221
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Motivated by the amount of code that goes unidentified on the web, we introduce a practical method for algorithmically identifying the programming language of source code. Our work is based on supervised learning and intelligent statistical features. We also explored, but abandoned, a grammatical approach. In testing, our implementation greatly outperforms that of an existing tool that relies on a Bayesian classifier. Code is written in Python and available under an MIT license.
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Algorithmic Programming Language Identification
| 2,222
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Mini-batch algorithms have been proposed as a way to speed-up stochastic convex optimization problems. We study how such algorithms can be improved using accelerated gradient methods. We provide a novel analysis, which shows how standard gradient methods may sometimes be insufficient to obtain a significant speed-up and propose a novel accelerated gradient algorithm, which deals with this deficiency, enjoys a uniformly superior guarantee and works well in practice.
|
Better Mini-Batch Algorithms via Accelerated Gradient Methods
| 2,223
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Shaping has proven to be a powerful but precarious means of improving reinforcement learning performance. Ng, Harada, and Russell (1999) proposed the potential-based shaping algorithm for adding shaping rewards in a way that guarantees the learner will learn optimal behavior. In this note, we prove certain similarities between this shaping algorithm and the initialization step required for several reinforcement learning algorithms. More specifically, we prove that a reinforcement learner with initial Q-values based on the shaping algorithm's potential function make the same updates throughout learning as a learner receiving potential-based shaping rewards. We further prove that under a broad category of policies, the behavior of these two learners are indistinguishable. The comparison provides intuition on the theoretical properties of the shaping algorithm as well as a suggestion for a simpler method for capturing the algorithm's benefit. In addition, the equivalence raises previously unaddressed issues concerning the efficiency of learning with potential-based shaping.
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Potential-Based Shaping and Q-Value Initialization are Equivalent
| 2,224
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We present IBSEAD or distributed autonomous entity systems based Interaction - a learning algorithm for the computer to self-evolve in a self-obsessed manner. This learning algorithm will present the computer to look at the internal and external environment in series of independent entities, which will interact with each other, with and/or without knowledge of the computer's brain. When a learning algorithm interacts, it does so by detecting and understanding the entities in the human algorithm. However, the problem with this approach is that the algorithm does not consider the interaction of the third party or unknown entities, which may be interacting with each other. These unknown entities in their interaction with the non-computer entities make an effect in the environment that influences the information and the behaviour of the computer brain. Such details and the ability to process the dynamic and unsettling nature of these interactions are absent in the current learning algorithm such as the decision tree learning algorithm. IBSEAD is able to evaluate and consider such algorithms and thus give us a better accuracy in simulation of the highly evolved nature of the human brain. Processes such as dreams, imagination and novelty, that exist in humans are not fully simulated by the existing learning algorithms. Also, Hidden Markov models (HMM) are useful in finding "hidden" entities, which may be known or unknown. However, this model fails to consider the case of unknown entities which maybe unclear or unknown. IBSEAD is better because it considers three types of entities- known, unknown and invisible. We present our case with a comparison of existing algorithms in known environments and cases and present the results of the experiments using dry run of the simulated runs of the existing machine learning algorithms versus IBSEAD.
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IBSEAD: - A Self-Evolving Self-Obsessed Learning Algorithm for Machine
Learning
| 2,225
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In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive} dependence on the logarithm of the number of kernels and the margin achieved by the classifier. However, there are some errors in parts of the proof which are corrected in this paper. Unfortunately, the final result turns out to be a risk bound which has a \emph{multiplicative} dependence on the logarithm of the number of kernels and the margin achieved by the classifier.
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A Note on Improved Loss Bounds for Multiple Kernel Learning
| 2,226
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Machine Learning (ML) techniques are indispensable in a wide range of fields. Unfortunately, the exponential increase of dataset sizes are rapidly extending the runtime of sequential algorithms and threatening to slow future progress in ML. With the promise of affordable large-scale parallel computing, Cloud systems offer a viable platform to resolve the computational challenges in ML. However, designing and implementing efficient, provably correct distributed ML algorithms is often prohibitively challenging. To enable ML researchers to easily and efficiently use parallel systems, we introduced the GraphLab abstraction which is designed to represent the computational patterns in ML algorithms while permitting efficient parallel and distributed implementations. In this paper we provide a formal description of the GraphLab parallel abstraction and present an efficient distributed implementation. We conduct a comprehensive evaluation of GraphLab on three state-of-the-art ML algorithms using real large-scale data and a 64 node EC2 cluster of 512 processors. We find that GraphLab achieves orders of magnitude performance gains over Hadoop while performing comparably or superior to hand-tuned MPI implementations.
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GraphLab: A Distributed Framework for Machine Learning in the Cloud
| 2,227
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For large scale learning problems, it is desirable if we can obtain the optimal model parameters by going through the data in only one pass. Polyak and Juditsky (1992) showed that asymptotically the test performance of the simple average of the parameters obtained by stochastic gradient descent (SGD) is as good as that of the parameters which minimize the empirical cost. However, to our knowledge, despite its optimal asymptotic convergence rate, averaged SGD (ASGD) received little attention in recent research on large scale learning. One possible reason is that it may take a prohibitively large number of training samples for ASGD to reach its asymptotic region for most real problems. In this paper, we present a finite sample analysis for the method of Polyak and Juditsky (1992). Our analysis shows that it indeed usually takes a huge number of samples for ASGD to reach its asymptotic region for improperly chosen learning rate. More importantly, based on our analysis, we propose a simple way to properly set learning rate so that it takes a reasonable amount of data for ASGD to reach its asymptotic region. We compare ASGD using our proposed learning rate with other well known algorithms for training large scale linear classifiers. The experiments clearly show the superiority of ASGD.
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Towards Optimal One Pass Large Scale Learning with Averaged Stochastic
Gradient Descent
| 2,228
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Discovering pattern sets or global patterns is an attractive issue from the pattern mining community in order to provide useful information. By combining local patterns satisfying a joint meaning, this approach produces patterns of higher level and thus more useful for the data analyst than the usual local patterns, while reducing the number of patterns. In parallel, recent works investigating relationships between data mining and constraint programming (CP) show that the CP paradigm is a nice framework to model and mine such patterns in a declarative and generic way. We present a constraint-based language which enables us to define queries addressing patterns sets and global patterns. The usefulness of such a declarative approach is highlighted by several examples coming from the clustering based on associations. This language has been implemented in the CP framework.
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Discovering Knowledge using a Constraint-based Language
| 2,229
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This paper gives specific divergence examples of value-iteration for several major Reinforcement Learning and Adaptive Dynamic Programming algorithms, when using a function approximator for the value function. These divergence examples differ from previous divergence examples in the literature, in that they are applicable for a greedy policy, i.e. in a "value iteration" scenario. Perhaps surprisingly, with a greedy policy, it is also possible to get divergence for the algorithms TD(1) and Sarsa(1). In addition to these divergences, we also achieve divergence for the Adaptive Dynamic Programming algorithms HDP, DHP and GDHP.
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The Divergence of Reinforcement Learning Algorithms with Value-Iteration
and Function Approximation
| 2,230
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We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our theory is for complete decision makers, which means that they have a complete set of preferences. Our main result shows that a complete rational decision maker implicitly has a probabilistic model of the environment. We have a countable version of this result that brings light on the issue of countable vs finite additivity by showing how it depends on the geometry of the space which we have preferences over. This is achieved through fruitfully connecting rationality with the Hahn-Banach Theorem. The theory presented here can be viewed as a formalization and extension of the betting odds approach to probability of Ramsey and De Finetti.
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Axioms for Rational Reinforcement Learning
| 2,231
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Building biological models by inferring functional dependencies from experimental data is an im- portant issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to increase the degree of automation. However, available ap- proaches often yield a single model only, rely on specific assumptions, and/or use dedicated, heuris- tic algorithms that are intolerant to changing circumstances or requirements in the view of the rapid progress made in Biotechnology. Our aim is to provide a declarative solution to the problem by ap- peal to Answer Set Programming (ASP) overcoming these difficulties. We build upon an existing approach to Automatic Network Reconstruction proposed by part of the authors. This approach has firm mathematical foundations and is well suited for ASP due to its combinatorial flavor providing a characterization of all models explaining a set of experiments. The usage of ASP has several ben- efits over the existing heuristic algorithms. First, it is declarative and thus transparent for biological experts. Second, it is elaboration tolerant and thus allows for an easy exploration and incorporation of biological constraints. Third, it allows for exploring the entire space of possible models. Finally, our approach offers an excellent performance, matching existing, special-purpose systems.
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Automatic Network Reconstruction using ASP
| 2,232
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Detecting changes in high-dimensional time series is difficult because it involves the comparison of probability densities that need to be estimated from finite samples. In this paper, we present the first feature extraction method tailored to change point detection, which is based on an extended version of Stationary Subspace Analysis. We reduce the dimensionality of the data to the most non-stationary directions, which are most informative for detecting state changes in the time series. In extensive simulations on synthetic data we show that the accuracy of three change point detection algorithms is significantly increased by a prior feature extraction step. These findings are confirmed in an application to industrial fault monitoring.
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Feature Extraction for Change-Point Detection using Stationary Subspace
Analysis
| 2,233
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We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We present simple and efficient algorithms for these problems: for Lasso and Ridge regression they need the same total number of attributes (up to constants) as do full-information algorithms, for reaching a certain accuracy. For Support-vector regression, we require exponentially less attributes compared to the state of the art. By that, we resolve an open problem recently posed by Cesa-Bianchi et al. (2010). Experiments show the theoretical bounds to be justified by superior performance compared to the state of the art.
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Optimal Algorithms for Ridge and Lasso Regression with Partially
Observed Attributes
| 2,234
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We consider online learning in partial-monitoring games against an oblivious adversary. We show that when the number of actions available to the learner is two and the game is nontrivial then it is reducible to a bandit-like game and thus the minimax regret is $\Theta(\sqrt{T})$.
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Non-trivial two-armed partial-monitoring games are bandits
| 2,235
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Kernel density estimation, a.k.a. Parzen windows, is a popular density estimation method, which can be used for outlier detection or clustering. With multivariate data, its performance is heavily reliant on the metric used within the kernel. Most earlier work has focused on learning only the bandwidth of the kernel (i.e., a scalar multiplicative factor). In this paper, we propose to learn a full Euclidean metric through an expectation-minimization (EM) procedure, which can be seen as an unsupervised counterpart to neighbourhood component analysis (NCA). In order to avoid overfitting with a fully nonparametric density estimator in high dimensions, we also consider a semi-parametric Gaussian-Parzen density model, where some of the variables are modelled through a jointly Gaussian density, while others are modelled through Parzen windows. For these two models, EM leads to simple closed-form updates based on matrix inversions and eigenvalue decompositions. We show empirically that our method leads to density estimators with higher test-likelihoods than natural competing methods, and that the metrics may be used within most unsupervised learning techniques that rely on such metrics, such as spectral clustering or manifold learning methods. Finally, we present a stochastic approximation scheme which allows for the use of this method in a large-scale setting.
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Local Component Analysis
| 2,236
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One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the identification of succinct, user-friendly properties that formally capture when certain clustering methods are preferred over others. Until now these properties focused on advantages of classical Linkage-Based algorithms, failing to identify when other clustering paradigms, such as popular center-based methods, are preferable. We present surprisingly simple new properties that delineate the differences between common clustering paradigms, which clearly and formally demonstrates advantages of center-based approaches for some applications. These properties address how sensitive algorithms are to changes in element frequencies, which we capture in a generalized setting where every element is associated with a real-valued weight.
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Weighted Clustering
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There has been increased interest in devising learning techniques that combine unlabeled data with labeled data ? i.e. semi-supervised learning. However, to the best of our knowledge, no study has been performed across various techniques and different types and amounts of labeled and unlabeled data. Moreover, most of the published work on semi-supervised learning techniques assumes that the labeled and unlabeled data come from the same distribution. It is possible for the labeling process to be associated with a selection bias such that the distributions of data points in the labeled and unlabeled sets are different. Not correcting for such bias can result in biased function approximation with potentially poor performance. In this paper, we present an empirical study of various semi-supervised learning techniques on a variety of datasets. We attempt to answer various questions such as the effect of independence or relevance amongst features, the effect of the size of the labeled and unlabeled sets and the effect of noise. We also investigate the impact of sample-selection bias on the semi-supervised learning techniques under study and implement a bivariate probit technique particularly designed to correct for such bias.
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Learning From Labeled And Unlabeled Data: An Empirical Study Across
Techniques And Domains
| 2,238
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The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an exponential number of mistakes even when learning simple functions. We then consider the question of whether kernel functions can analogously be used to run the multiplicative-update Winnow algorithm over an expanded feature space of exponentially many conjunctions. Known upper bounds imply that the Winnow algorithm can learn Disjunctive Normal Form (DNF) formulae with a polynomial mistake bound in this setting. However, we prove that it is computationally hard to simulate Winnows behavior for learning DNF over such a feature set. This implies that the kernel functions which correspond to running Winnow for this problem are not efficiently computable, and that there is no general construction that can run Winnow with kernels.
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Efficiency versus Convergence of Boolean Kernels for On-Line Learning
Algorithms
| 2,239
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In this paper, we consider Markov Decision Processes (MDPs) with error states. Error states are those states entering which is undesirable or dangerous. We define the risk with respect to a policy as the probability of entering such a state when the policy is pursued. We consider the problem of finding good policies whose risk is smaller than some user-specified threshold, and formalize it as a constrained MDP with two criteria. The first criterion corresponds to the value function originally given. We will show that the risk can be formulated as a second criterion function based on a cumulative return, whose definition is independent of the original value function. We present a model free, heuristic reinforcement learning algorithm that aims at finding good deterministic policies. It is based on weighting the original value function and the risk. The weight parameter is adapted in order to find a feasible solution for the constrained problem that has a good performance with respect to the value function. The algorithm was successfully applied to the control of a feed tank with stochastic inflows that lies upstream of a distillation column. This control task was originally formulated as an optimal control problem with chance constraints, and it was solved under certain assumptions on the model to obtain an optimal solution. The power of our learning algorithm is that it can be used even when some of these restrictive assumptions are relaxed.
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Risk-Sensitive Reinforcement Learning Applied to Control under
Constraints
| 2,240
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We consider a bandit problem over a graph where the rewards are not directly observed. Instead, the decision maker can compare two nodes and receive (stochastic) information pertaining to the difference in their value. The graph structure describes the set of possible comparisons. Consequently, comparing between two nodes that are relatively far requires estimating the difference between every pair of nodes on the path between them. We analyze this problem from the perspective of sample complexity: How many queries are needed to find an approximately optimal node with probability more than $1-\delta$ in the PAC setup? We show that the topology of the graph plays a crucial in defining the sample complexity: graphs with a low diameter have a much better sample complexity.
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Bandits with an Edge
| 2,241
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User profiling is a useful primitive for constructing personalised services, such as content recommendation. In the present paper we investigate the feasibility of user profiling in a distributed setting, with no central authority and only local information exchanges between users. We compute a profile vector for each user (i.e., a low-dimensional vector that characterises her taste) via spectral transformation of observed user-produced ratings for items. Our two main contributions follow: i) We consider a low-rank probabilistic model of user taste. More specifically, we consider that users and items are partitioned in a constant number of classes, such that users and items within the same class are statistically identical. We prove that without prior knowledge of the compositions of the classes, based solely on few random observed ratings (namely $O(N\log N)$ such ratings for $N$ users), we can predict user preference with high probability for unrated items by running a local vote among users with similar profile vectors. In addition, we provide empirical evaluations characterising the way in which spectral profiling performance depends on the dimension of the profile space. Such evaluations are performed on a data set of real user ratings provided by Netflix. ii) We develop distributed algorithms which provably achieve an embedding of users into a low-dimensional space, based on spectral transformation. These involve simple message passing among users, and provably converge to the desired embedding. Our method essentially relies on a novel combination of gossiping and the algorithm proposed by Oja and Karhunen.
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Distributed User Profiling via Spectral Methods
| 2,242
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Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper represents LDA as a factor graph within the Markov random field (MRF) framework, which enables the classic loopy belief propagation (BP) algorithm for approximate inference and parameter estimation. Although two commonly-used approximate inference methods, such as variational Bayes (VB) and collapsed Gibbs sampling (GS), have gained great successes in learning LDA, the proposed BP is competitive in both speed and accuracy as validated by encouraging experimental results on four large-scale document data sets. Furthermore, the BP algorithm has the potential to become a generic learning scheme for variants of LDA-based topic models. To this end, we show how to learn two typical variants of LDA-based topic models, such as author-topic models (ATM) and relational topic models (RTM), using BP based on the factor graph representation.
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Learning Topic Models by Belief Propagation
| 2,243
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In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex structures in order to represent data in a more natural way. Terms are the basis for functional and logic programming representation. Distances between terms are a useful tool not only to compare terms, but also to determine the search space in many of these applications. This dissertation applies distances between terms, exploiting the features of each distance and the possibility to compare from propositional data types to hierarchical representations. The distances between terms are applied through the k-NN (k-nearest neighbor) classification algorithm using XML as a common language representation. To be able to represent these data in an XML structure and to take advantage of the benefits of distance between terms, it is necessary to apply some transformations. These transformations allow the conversion of flat data into hierarchical data represented in XML, using some techniques based on intuitive associations between the names and values of variables and associations based on attribute similarity. Several experiments with the distances between terms of Nienhuys-Cheng and Estruch et al. were performed. In the case of originally propositional data, these distances are compared to the Euclidean distance. In all cases, the experiments were performed with the distance-weighted k-nearest neighbor algorithm, using several exponents for the attraction function (weighted distance). It can be seen that in some cases, the term distances can significantly improve the results on approaches applied to flat representations.
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Application of distances between terms for flat and hierarchical data
| 2,244
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In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an ${\bf unobservable}$ training set which is noise-free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with the ideal noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper we analyze the noise tolerance properties of risk minimization (under different loss functions), which is a generic method for learning classifiers. We show that risk minimization under 0-1 loss function has impressive noise tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude the paper with some discussion on implications of these theoretical results.
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Noise Tolerance under Risk Minimization
| 2,245
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Active learners alleviate the burden of labeling large amounts of data by detecting and asking the user to label only the most informative examples in the domain. We focus here on active learning for multi-view domains, in which there are several disjoint subsets of features (views), each of which is sufficient to learn the target concept. In this paper we make several contributions. First, we introduce Co-Testing, which is the first approach to multi-view active learning. Second, we extend the multi-view learning framework by also exploiting weak views, which are adequate only for learning a concept that is more general/specific than the target concept. Finally, we empirically show that Co-Testing outperforms existing active learners on a variety of real world domains such as wrapper induction, Web page classification, advertisement removal, and discourse tree parsing.
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Active Learning with Multiple Views
| 2,246
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Recently, a unified framework for adaptive kernel based signal processing of complex data was presented by the authors, which, besides offering techniques to map the input data to complex Reproducing Kernel Hilbert Spaces, developed a suitable Wirtinger-like Calculus for general Hilbert Spaces. In this short paper, the extended Wirtinger's calculus is adopted to derive complex kernel-based widely-linear estimation filters. Furthermore, we illuminate several important characteristics of the widely linear filters. We show that, although in many cases the gains from adopting widely linear estimation filters, as alternatives to ordinary linear ones, are rudimentary, for the case of kernel based widely linear filters significant performance improvements can be obtained.
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The Augmented Complex Kernel LMS
| 2,247
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Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle changing user preferences over time. Recent proposals to address this issue are heuristic in nature and do not fully exploit the time-dependent structure of the problem. As a principled and general temporal formulation, we propose a dynamical state space model of matrix factorization. Our proposal builds upon probabilistic matrix factorization, a Bayesian model with Gaussian priors. We utilize results in state tracking, such as the Kalman filter, to provide accurate recommendations in the presence of both process and measurement noise. We show how system parameters can be learned via expectation-maximization and provide comparisons to current published techniques.
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Dynamic Matrix Factorization: A State Space Approach
| 2,248
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The disagreement coefficient of Hanneke has become a central data independent invariant in proving active learning rates. It has been shown in various ways that a concept class with low complexity together with a bound on the disagreement coefficient at an optimal solution allows active learning rates that are superior to passive learning ones. We present a different tool for pool based active learning which follows from the existence of a certain uniform version of low disagreement coefficient, but is not equivalent to it. In fact, we present two fundamental active learning problems of significant interest for which our approach allows nontrivial active learning bounds. However, any general purpose method relying on the disagreement coefficient bounds only fails to guarantee any useful bounds for these problems. The tool we use is based on the learner's ability to compute an estimator of the difference between the loss of any hypotheses and some fixed "pivotal" hypothesis to within an absolute error of at most $\eps$ times the
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Active Learning Using Smooth Relative Regret Approximations with
Applications
| 2,249
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The analysis of physiological processes over time are often given by spectrometric or gene expression profiles over time with only few time points but a large number of measured variables. The analysis of such temporal sequences is challenging and only few methods have been proposed. The information can be encoded time independent, by means of classical expression differences for a single time point or in expression profiles over time. Available methods are limited to unsupervised and semi-supervised settings. The predictive variables can be identified only by means of wrapper or post-processing techniques. This is complicated due to the small number of samples for such studies. Here, we present a supervised learning approach, termed Supervised Topographic Mapping Through Time (SGTM-TT). It learns a supervised mapping of the temporal sequences onto a low dimensional grid. We utilize a hidden markov model (HMM) to account for the time domain and relevance learning to identify the relevant feature dimensions most predictive over time. The learned mapping can be used to visualize the temporal sequences and to predict the class of a new sequence. The relevance learning permits the identification of discriminating masses or gen expressions and prunes dimensions which are unnecessary for the classification task or encode mainly noise. In this way we obtain a very efficient learning system for temporal sequences. The results indicate that using simultaneous supervised learning and metric adaptation significantly improves the prediction accuracy for synthetically and real life data in comparison to the standard techniques. The discriminating features, identified by relevance learning, compare favorably with the results of alternative methods. Our method permits the visualization of the data on a low dimensional grid, highlighting the observed temporal structure.
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Supervised learning of short and high-dimensional temporal sequences for
life science measurements
| 2,250
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Bayesian optimization (BO) algorithms try to optimize an unknown function that is expensive to evaluate using minimum number of evaluations/experiments. Most of the proposed algorithms in BO are sequential, where only one experiment is selected at each iteration. This method can be time inefficient when each experiment takes a long time and more than one experiment can be ran concurrently. On the other hand, requesting a fix-sized batch of experiments at each iteration causes performance inefficiency in BO compared to the sequential policies. In this paper, we present an algorithm that asks a batch of experiments at each time step t where the batch size p_t is dynamically determined in each step. Our algorithm is based on the observation that the sequence of experiments selected by the sequential policy can sometimes be almost independent from each other. Our algorithm identifies such scenarios and request those experiments at the same time without degrading the performance. We evaluate our proposed method using the Expected Improvement policy and the results show substantial speedup with little impact on the performance in eight real and synthetic benchmarks.
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Dynamic Batch Bayesian Optimization
| 2,251
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This report considers how to inject external candidate solutions into the CMA-ES algorithm. The injected solutions might stem from a gradient or a Newton step, a surrogate model optimizer or any other oracle or search mechanism. They can also be the result of a repair mechanism, for example to render infeasible solutions feasible. Only small modifications to the CMA-ES are necessary to turn injection into a reliable and effective method: too long steps need to be tightly renormalized. The main objective of this report is to reveal this simple mechanism. Depending on the source of the injected solutions, interesting variants of CMA-ES arise. When the best-ever solution is always (re-)injected, an elitist variant of CMA-ES with weighted multi-recombination arises. When \emph{all} solutions are injected from an \emph{external} source, the resulting algorithm might be viewed as \emph{adaptive encoding} with step-size control. In first experiments, injected solutions of very good quality lead to a convergence speed twice as fast as on the (simple) sphere function without injection. This means that we observe an impressive speed-up on otherwise difficult to solve functions. Single bad injected solutions on the other hand do no significant harm.
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Injecting External Solutions Into CMA-ES
| 2,252
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We propose a method to efficiently construct data-dependent kernels which can make use of large quantities of (unlabeled) data. Our construction makes an approximation in the standard construction of semi-supervised kernels in Sindhwani et al. 2005. In typical cases these kernels can be computed in nearly-linear time (in the amount of data), improving on the cubic time of the standard construction, enabling large scale semi-supervised learning in a variety of contexts. The methods are validated on semi-supervised and unsupervised problems on data sets containing upto 64,000 sample points.
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Data-dependent kernels in nearly-linear time
| 2,253
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Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class of convex penalties introduced in the machine learning community, which take the form of a sum of l_2 and l_infinity-norms over groups of variables. They extend the classical group-sparsity regularization in the sense that the groups possibly overlap, allowing more flexibility in the group design. We review efficient optimization methods to deal with the corresponding inverse problems, and their application to the problem of learning dictionaries of natural image patches: On the one hand, dictionary learning has indeed proven effective for various signal processing tasks. On the other hand, structured sparsity provides a natural framework for modeling dependencies between dictionary elements. We thus consider a structured sparse regularization to learn dictionaries embedded in a particular structure, for instance a tree or a two-dimensional grid. In the latter case, the results we obtain are similar to the dictionaries produced by topographic independent component analysis.
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Learning Hierarchical and Topographic Dictionaries with Structured
Sparsity
| 2,254
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In this paper, we describe our approach to the Wikipedia Participation Challenge which aims to predict the number of edits a Wikipedia editor will make in the next 5 months. The best submission from our team, "zeditor", achieved 41.7% improvement over WMF's baseline predictive model and the final rank of 3rd place among 96 teams. An interesting characteristic of our approach is that only temporal dynamics features (i.e., how the number of edits changes in recent periods, etc.) are used in a self-supervised learning framework, which makes it easy to be generalised to other application domains.
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Wikipedia Edit Number Prediction based on Temporal Dynamics Only
| 2,255
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This paper presents a method of choosing number of states of a HMM based on number of critical points of the motion capture data. The choice of Hidden Markov Models(HMM) parameters is crucial for recognizer's performance as it is the first step of the training and cannot be corrected automatically within HMM. In this article we define predictor of number of states based on number of critical points of the sequence and test its effectiveness against sample data.
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Deciding of HMM parameters based on number of critical points for
gesture recognition from motion capture data
| 2,256
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We develop a new tool for data-dependent analysis of the exploration-exploitation trade-off in learning under limited feedback. Our tool is based on two main ingredients. The first ingredient is a new concentration inequality that makes it possible to control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. The second ingredient is an application of this inequality to the exploration-exploitation trade-off via importance weighted sampling. We apply the new tool to the stochastic multiarmed bandit problem, however, the main importance of this paper is the development and understanding of the new tool rather than improvement of existing algorithms for stochastic multiarmed bandits. In the follow-up work we demonstrate that the new tool can improve over state-of-the-art in structurally richer problems, such as stochastic multiarmed bandits with side information (Seldin et al., 2011a).
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PAC-Bayes-Bernstein Inequality for Martingales and its Application to
Multiarmed Bandits
| 2,257
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Structured classification tasks such as sequence labeling and dependency parsing have seen much interest by the Natural Language Processing and the machine learning communities. Several online learning algorithms were adapted for structured tasks such as Perceptron, Passive- Aggressive and the recently introduced Confidence-Weighted learning . These online algorithms are easy to implement, fast to train and yield state-of-the-art performance. However, unlike probabilistic models like Hidden Markov Model and Conditional random fields, these methods generate models that output merely a prediction with no additional information regarding confidence in the correctness of the output. In this work we fill the gap proposing few alternatives to compute the confidence in the output of non-probabilistic algorithms.We show how to compute confidence estimates in the prediction such that the confidence reflects the probability that the word is labeled correctly. We then show how to use our methods to detect mislabeled words, trade recall for precision and active learning. We evaluate our methods on four noun-phrase chunking and named entity recognition sequence labeling tasks, and on dependency parsing for 14 languages.
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Confidence Estimation in Structured Prediction
| 2,258
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In this paper we propose and study a generalization of the standard active-learning model where a more general type of query, class conditional query, is allowed. Such queries have been quite useful in applications, but have been lacking theoretical understanding. In this work, we characterize the power of such queries under two well-known noise models. We give nearly tight upper and lower bounds on the number of queries needed to learn both for the general agnostic setting and for the bounded noise model. We further show that our methods can be made adaptive to the (unknown) noise rate, with only negligible loss in query complexity.
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Robust Interactive Learning
| 2,259
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In this paper, we consider the problem of multi-armed bandits with a large, possibly infinite number of correlated arms. We assume that the arms have Bernoulli distributed rewards, independent across time, where the probabilities of success are parametrized by known attribute vectors for each arm, as well as an unknown preference vector, each of dimension $n$. For this model, we seek an algorithm with a total regret that is sub-linear in time and independent of the number of arms. We present such an algorithm, which we call the Two-Phase Algorithm, and analyze its performance. We show upper bounds on the total regret which applies uniformly in time, for both the finite and infinite arm cases. The asymptotics of the finite arm bound show that for any $f \in \omega(\log(T))$, the total regret can be made to be $O(n \cdot f(T))$. In the infinite arm case, the total regret is $O(\sqrt{n^3 T})$.
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Parametrized Stochastic Multi-armed Bandits with Binary Rewards
| 2,260
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We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the observed data --- after performing structural risk minimization to avoid overfitting. We obtain finite-sample risk bounds with minimal structural and noise assumptions, and a natural speed-precision tradeoff. The offline (learning) and online (prediction) stages can be solved by convex programming, but this naive approach has runtime complexity $O(n^3)$, which is prohibitive for large datasets. We design instead a regression algorithm whose speed and generalization performance depend on the intrinsic dimension of the data, to which the algorithm adapts. While our main innovation is algorithmic, the statistical results may also be of independent interest.
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Efficient Regression in Metric Spaces via Approximate Lipschitz
Extension
| 2,261
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Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for large scale systems. Recently, many methods have been proposed to accelerate the computational time of spectral clustering. These approximate methods usually involve sampling techniques by which a lot information of the original data may be lost. In this work, we propose a fast and accurate spectral clustering approach using an approximate commute time embedding, which is similar to the spectral embedding. The method does not require using any sampling technique and computing any eigenvector at all. Instead it uses random projection and a linear time solver to find the approximate embedding. The experiments in several synthetic and real datasets show that the proposed approach has better clustering quality and is faster than the state-of-the-art approximate spectral clustering methods.
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Large Scale Spectral Clustering Using Approximate Commute Time Embedding
| 2,262
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In this paper we propose a framework for solving constrained online convex optimization problem. Our motivation stems from the observation that most algorithms proposed for online convex optimization require a projection onto the convex set $\mathcal{K}$ from which the decisions are made. While for simple shapes (e.g. Euclidean ball) the projection is straightforward, for arbitrary complex sets this is the main computational challenge and may be inefficient in practice. In this paper, we consider an alternative online convex optimization problem. Instead of requiring decisions belong to $\mathcal{K}$ for all rounds, we only require that the constraints which define the set $\mathcal{K}$ be satisfied in the long run. We show that our framework can be utilized to solve a relaxed version of online learning with side constraints addressed in \cite{DBLP:conf/colt/MannorT06} and \cite{DBLP:conf/aaai/KvetonYTM08}. By turning the problem into an online convex-concave optimization problem, we propose an efficient algorithm which achieves $\tilde{\mathcal{O}}(\sqrt{T})$ regret bound and $\tilde{\mathcal{O}}(T^{3/4})$ bound for the violation of constraints. Then we modify the algorithm in order to guarantee that the constraints are satisfied in the long run. This gain is achieved at the price of getting $\tilde{\mathcal{O}}(T^{3/4})$ regret bound. Our second algorithm is based on the Mirror Prox method \citep{nemirovski-2005-prox} to solve variational inequalities which achieves $\tilde{\mathcal{\mathcal{O}}}(T^{2/3})$ bound for both regret and the violation of constraints when the domain $\K$ can be described by a finite number of linear constraints. Finally, we extend the result to the setting where we only have partial access to the convex set $\mathcal{K}$ and propose a multipoint bandit feedback algorithm with the same bounds in expectation as our first algorithm.
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Trading Regret for Efficiency: Online Convex Optimization with Long Term
Constraints
| 2,263
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In citep{Hazan-2008-extract}, the authors showed that the regret of online linear optimization can be bounded by the total variation of the cost vectors. In this paper, we extend this result to general online convex optimization. We first analyze the limitations of the algorithm in \citep{Hazan-2008-extract} when applied it to online convex optimization. We then present two algorithms for online convex optimization whose regrets are bounded by the variation of cost functions. We finally consider the bandit setting, and present a randomized algorithm for online bandit convex optimization with a variation-based regret bound. We show that the regret bound for online bandit convex optimization is optimal when the variation of cost functions is independent of the number of trials.
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Regret Bound by Variation for Online Convex Optimization
| 2,264
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Although exploratory behaviors are ubiquitous in the animal kingdom, their computational underpinnings are still largely unknown. Behavioral Psychology has identified learning as a primary drive underlying many exploratory behaviors. Exploration is seen as a means for an animal to gather sensory data useful for reducing its ignorance about the environment. While related problems have been addressed in Data Mining and Reinforcement Learning, the computational modeling of learning-driven exploration by embodied agents is largely unrepresented. Here, we propose a computational theory for learning-driven exploration based on the concept of missing information that allows an agent to identify informative actions using Bayesian inference. We demonstrate that when embodiment constraints are high, agents must actively coordinate their actions to learn efficiently. Compared to earlier approaches, our exploration policy yields more efficient learning across a range of worlds with diverse structures. The improved learning in turn affords greater success in general tasks including navigation and reward gathering. We conclude by discussing how the proposed theory relates to previous information-theoretic objectives of behavior, such as predictive information and the free energy principle, and how it might contribute to a general theory of exploratory behavior.
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Learning in embodied action-perception loops through exploration
| 2,265
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This paper derives an identity connecting the square loss of ridge regression in on-line mode with the loss of the retrospectively best regressor. Some corollaries about the properties of the cumulative loss of on-line ridge regression are also obtained.
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An Identity for Kernel Ridge Regression
| 2,266
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Unsupervised aggregation of independently built univariate predictors is explored as an alternative regularization approach for noisy, sparse datasets. Bipartite ranking algorithm Smooth Rank implementing this approach is introduced. The advantages of this algorithm are demonstrated on two types of problems. First, Smooth Rank is applied to two-class problems from bio-medical field, where ranking is often preferable to classification. In comparison against SVMs with radial and linear kernels, Smooth Rank had the best performance on 8 out of 12 benchmark benchmarks. The second area of application is survival analysis, which is reduced here to bipartite ranking in a way which allows one to use commonly accepted measures of methods performance. In comparison of Smooth Rank with Cox PH regression and CoxPath methods, Smooth Rank proved to be the best on 9 out of 10 benchmark datasets.
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Bipartite ranking algorithm for classification and survival analysis
| 2,267
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We investigate a recently proposed family of positive-definite kernels that mimic the computation in large neural networks. We examine the properties of these kernels using tools from differential geometry; specifically, we analyze the geometry of surfaces in Hilbert space that are induced by these kernels. When this geometry is described by a Riemannian manifold, we derive results for the metric, curvature, and volume element. Interestingly, though, we find that the simplest kernel in this family does not admit such an interpretation. We explore two variations of these kernels that mimic computation in neural networks with different activation functions. We experiment with these new kernels on several data sets and highlight their general trends in performance for classification.
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Analysis and Extension of Arc-Cosine Kernels for Large Margin
Classification
| 2,268
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We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower dimensionality, our approach aims to preserve the nonnegative components of the data that are important for classification. We identify these components from the support vectors of large-margin classifiers and derive iterative updates to preserve them in a semi-supervised version of NMF. These updates have a simple multiplicative form like their unsupervised counterparts; they are also guaranteed at each iteration to decrease their loss function---a weighted sum of I-divergences that captures the trade-off between unsupervised and supervised learning. We evaluate these updates for dimensionality reduction when they are used as a precursor to linear classification. In this role, we find that they yield much better performance than their unsupervised counterparts. We also find one unexpected benefit of the low dimensional representations discovered by our approach: often they yield more accurate classifiers than both ordinary and transductive SVMs trained in the original input space.
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Nonnegative Matrix Factorization for Semi-supervised Dimensionality
Reduction
| 2,269
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This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering objective, so clustering aspect of the NMF has a solid justification. Different from previous approaches which usually discard the nonnegativity constraints, our approach guarantees the stationary point being used in deriving the equivalence is located on the feasible region in the nonnegative orthant. Additionally, since clustering capability of a matrix decomposition technique can sometimes imply its latent semantic indexing (LSI) aspect, we will also evaluate LSI aspect of the NMF by showing its capability in solving the synonymy and polysemy problems in synthetic datasets. And more extensive evaluation will be conducted by comparing LSI performances of the NMF and the singular value decomposition (SVD), the standard LSI method, using some standard datasets.
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Clustering and Latent Semantic Indexing Aspects of the Nonnegative
Matrix Factorization
| 2,270
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The selection of the best classification algorithm for a given dataset is a very widespread problem, occuring each time one has to choose a classifier to solve a real-world problem. It is also a complex task with many important methodological decisions to make. Among those, one of the most crucial is the choice of an appropriate measure in order to properly assess the classification performance and rank the algorithms. In this article, we focus on this specific task. We present the most popular measures and compare their behavior through discrimination plots. We then discuss their properties from a more theoretical perspective. It turns out several of them are equivalent for classifiers comparison purposes. Futhermore. they can also lead to interpretation problems. Among the numerous measures proposed over the years, it appears that the classical overall success rate and marginal rates are the more suitable for classifier comparison task.
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Evaluation of Performance Measures for Classifiers Comparison
| 2,271
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We propose a new, nonparametric approach to estimating the value function in reinforcement learning. This approach makes use of a recently developed representation of conditional distributions as functions in a reproducing kernel Hilbert space. Such representations bypass the need for estimating transition probabilities, and apply to any domain on which kernels can be defined. Our approach avoids the need to approximate intractable integrals since expectations are represented as RKHS inner products whose computation has linear complexity in the sample size. Thus, we can efficiently perform value function estimation in a wide variety of settings, including finite state spaces, continuous states spaces, and partially observable tasks where only sensor measurements are available. A second advantage of the approach is that we learn the conditional distribution representation from a training sample, and do not require an exhaustive exploration of the state space. We prove convergence of our approach either to the optimal policy, or to the closest projection of the optimal policy in our model class, under reasonable assumptions. In experiments, we demonstrate the performance of our algorithm on a learning task in a continuous state space (the under-actuated pendulum), and on a navigation problem where only images from a sensor are observed. We compare with least-squares policy iteration where a Gaussian process is used for value function estimation. Our algorithm achieves better performance in both tasks.
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Modeling transition dynamics in MDPs with RKHS embeddings of conditional
distributions
| 2,272
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Selecting the best classifier among the available ones is a difficult task, especially when only instances of one class exist. In this work we examine the notion of combining one-class classifiers as an alternative for selecting the best classifier. In particular, we propose two new one-class classification performance measures to weigh classifiers and show that a simple ensemble that implements these measures can outperform the most popular one-class ensembles. Furthermore, we propose a new one-class ensemble scheme, TUPSO, which uses meta-learning to combine one-class classifiers. Our experiments demonstrate the superiority of TUPSO over all other tested ensembles and show that the TUPSO performance is statistically indistinguishable from that of the hypothetical best classifier.
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Combining One-Class Classifiers via Meta-Learning
| 2,273
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We consider the problem of building high-level, class-specific feature detectors from only unlabeled data. For example, is it possible to learn a face detector using only unlabeled images? To answer this, we train a 9-layered locally connected sparse autoencoder with pooling and local contrast normalization on a large dataset of images (the model has 1 billion connections, the dataset has 10 million 200x200 pixel images downloaded from the Internet). We train this network using model parallelism and asynchronous SGD on a cluster with 1,000 machines (16,000 cores) for three days. Contrary to what appears to be a widely-held intuition, our experimental results reveal that it is possible to train a face detector without having to label images as containing a face or not. Control experiments show that this feature detector is robust not only to translation but also to scaling and out-of-plane rotation. We also find that the same network is sensitive to other high-level concepts such as cat faces and human bodies. Starting with these learned features, we trained our network to obtain 15.8% accuracy in recognizing 20,000 object categories from ImageNet, a leap of 70% relative improvement over the previous state-of-the-art.
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Building high-level features using large scale unsupervised learning
| 2,274
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Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that solving a two-manifold problem can aid in learning a nonlinear dynamical system from limited data.
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Two-Manifold Problems
| 2,275
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Traditional Reinforcement Learning (RL) has focused on problems involving many states and few actions, such as simple grid worlds. Most real world problems, however, are of the opposite type, Involving Few relevant states and many actions. For example, to return home from a conference, humans identify only few subgoal states such as lobby, taxi, airport etc. Each valid behavior connecting two such states can be viewed as an action, and there are trillions of them. Assuming the subgoal identification problem is already solved, the quality of any RL method---in real-world settings---depends less on how well it scales with the number of states than on how well it scales with the number of actions. This is where our new method T-Learning excels, by evaluating the relatively few possible transits from one state to another in a policy-independent way, rather than a huge number of state-action pairs, or states in traditional policy-dependent ways. Illustrative experiments demonstrate that performance improvements of T-Learning over Q-learning can be arbitrarily large.
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T-Learning
| 2,276
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Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational biology. This paper introduces a topic modeling toolbox (TMBP) based on the belief propagation (BP) algorithms. TMBP toolbox is implemented by MEX C++/Matlab/Octave for either Windows 7 or Linux. Compared with existing topic modeling packages, the novelty of this toolbox lies in the BP algorithms for learning LDA-based topic models. The current version includes BP algorithms for latent Dirichlet allocation (LDA), author-topic models (ATM), relational topic models (RTM), and labeled LDA (LaLDA). This toolbox is an ongoing project and more BP-based algorithms for various topic models will be added in the near future. Interested users may also extend BP algorithms for learning more complicated topic models. The source codes are freely available under the GNU General Public Licence, Version 1.0 at https://mloss.org/software/view/399/.
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A Topic Modeling Toolbox Using Belief Propagation
| 2,277
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Leveraging the power of increasing amounts of data to analyze customer base for attracting and retaining the most valuable customers is a major problem facing companies in this information age. Data mining technologies extract hidden information and knowledge from large data stored in databases or data warehouses, thereby supporting the corporate decision making process. CRM uses data mining (one of the elements of CRM) techniques to interact with customers. This study investigates the use of a technique, semi-supervised learning, for the management and analysis of customer-related data warehouse and information. The idea of semi-supervised learning is to learn not only from the labeled training data, but to exploit also the structural information in additionally available unlabeled data. The proposed semi-supervised method is a model by means of a feed-forward neural network trained by a back propagation algorithm (multi-layer perceptron) in order to predict the category of an unknown customer (potential customers). In addition, this technique can be used with Rapid Miner tools for both labeled and unlabeled data.
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Customers Behavior Modeling by Semi-Supervised Learning in Customer
Relationship Management
| 2,278
|
Diabetes is a major health problem in both developing and developed countries and its incidence is rising dramatically. In this study, we investigate a novel automatic approach to diagnose Diabetes disease based on Feature Weighted Support Vector Machines (FW-SVMs) and Modified Cuckoo Search (MCS). The proposed model consists of three stages: Firstly, PCA is applied to select an optimal subset of features out of set of all the features. Secondly, Mutual Information is employed to construct the FWSVM by weighting different features based on their degree of importance. Finally, since parameter selection plays a vital role in classification accuracy of SVMs, MCS is applied to select the best parameter values. The proposed MI-MCS-FWSVM method obtains 93.58% accuracy on UCI dataset. The experimental results demonstrate that our method outperforms the previous methods by not only giving more accurate results but also significantly speeding up the classification procedure.
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Automatic Detection of Diabetes Diagnosis using Feature Weighted Support
Vector Machines based on Mutual Information and Modified Cuckoo Search
| 2,279
|
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish convergence guarantees. The overall learning procedure has the nice properties that a) the learned conical combination is automatically designed to perform the regression task at hand and b) the updates implicated by the optimization procedure are quite inexpensive. In order to shed light on the appositeness of our learning strategy, we present empirical results from experiments conducted on various benchmark datasets.
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Stochastic Low-Rank Kernel Learning for Regression
| 2,280
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Teaching is one of the most important factors affecting any education system. Many research efforts have been conducted to facilitate the presentation modes used by instructors in classrooms as well as provide means for students to review lectures through web browsers. Other studies have been made to provide acoustical design recommendations for classrooms like room size and reverberation times. However, using acoustical features of classrooms as a way to provide education systems with feedback about the learning process was not thoroughly investigated in any of these studies. We propose a system that extracts different sound features of students and instructors, and then uses machine learning techniques to evaluate the acoustical quality of any learning environment. We infer conclusions about the students' satisfaction with the quality of lectures. Using classifiers instead of surveys and other subjective ways of measures can facilitate and speed such experiments which enables us to perform them continuously. We believe our system enables education systems to continuously review and improve their teaching strategies and acoustical quality of classrooms.
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Acoustical Quality Assessment of the Classroom Environment
| 2,281
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We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or a strongly convex regularizer, making them unsuitable for non-smooth optimization. We develop a simple yet efficient method for a family of non-smooth optimization problems where the dual form of the loss function is bilinear in primal and dual variables. We cast a non-smooth optimization problem into a minimax optimization problem, and develop a primal dual prox method that solves the minimax optimization problem at a rate of $O(1/T)$ {assuming that the proximal step can be efficiently solved}, significantly faster than a standard subgradient descent method that has an $O(1/\sqrt{T})$ convergence rate. Our empirical study verifies the efficiency of the proposed method for various non-smooth optimization problems that arise ubiquitously in machine learning by comparing it to the state-of-the-art first order methods.
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An Efficient Primal-Dual Prox Method for Non-Smooth Optimization
| 2,282
|
In the current competitive world, industrial companies seek to manufacture products of higher quality which can be achieved by increasing reliability, maintainability and thus the availability of products. On the other hand, improvement in products lifecycle is necessary for achieving high reliability. Typically, maintenance activities are aimed to reduce failures of industrial machinery and minimize the consequences of such failures. So the industrial companies try to improve their efficiency by using different fault detection techniques. One strategy is to process and analyze previous generated data to predict future failures. The purpose of this paper is to detect wasted parts using different data mining algorithms and compare the accuracy of these algorithms. A combination of thermal and physical characteristics has been used and the algorithms were implemented on Ahanpishegan's current data to estimate the availability of its produced parts. Keywords: Data Mining, Fault Detection, Availability, Prediction Algorithms.
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A Comparison Between Data Mining Prediction Algorithms for Fault
Detection(Case study: Ahanpishegan co.)
| 2,283
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Clustering is considered a non-supervised learning setting, in which the goal is to partition a collection of data points into disjoint clusters. Often a bound $k$ on the number of clusters is given or assumed by the practitioner. Many versions of this problem have been defined, most notably $k$-means and $k$-median. An underlying problem with the unsupervised nature of clustering it that of determining a similarity function. One approach for alleviating this difficulty is known as clustering with side information, alternatively, semi-supervised clustering. Here, the practitioner incorporates side information in the form of "must be clustered" or "must be separated" labels for data point pairs. Each such piece of information comes at a "query cost" (often involving human response solicitation). The collection of labels is then incorporated in the usual clustering algorithm as either strict or as soft constraints, possibly adding a pairwise constraint penalty function to the chosen clustering objective. Our work is mostly related to clustering with side information. We ask how to choose the pairs of data points. Our analysis gives rise to a method provably better than simply choosing them uniformly at random. Roughly speaking, we show that the distribution must be biased so as more weight is placed on pairs incident to elements in smaller clusters in some optimal solution. Of course we do not know the optimal solution, hence we don't know the bias. Using the recently introduced method of $\eps$-smooth relative regret approximations of Ailon, Begleiter and Ezra, we can show an iterative process that improves both the clustering and the bias in tandem. The process provably converges to the optimal solution faster (in terms of query cost) than an algorithm selecting pairs uniformly.
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Active Learning of Custering with Side Information Using $\eps$-Smooth
Relative Regret Approximations
| 2,284
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Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Under this assumption, we show three things. We present a new algorithm---Regressor Elimination--- with a regret similar to the agnostic setting (i.e. in the absence of realizability assumption). We prove a new lower bound showing no algorithm can achieve superior performance in the worst case even with the realizability assumption. However, we do show that for any set of policies (mapping contexts to actions), there is a distribution over rewards (given context) such that our new algorithm has constant regret unlike the previous approaches.
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Contextual Bandit Learning with Predictable Rewards
| 2,285
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Inverse reinforcement learning (IRL) addresses the problem of recovering a task description given a demonstration of the optimal policy used to solve such a task. The optimal policy is usually provided by an expert or teacher, making IRL specially suitable for the problem of apprenticeship learning. The task description is encoded in the form of a reward function of a Markov decision process (MDP). Several algorithms have been proposed to find the reward function corresponding to a set of demonstrations. One of the algorithms that has provided best results in different applications is a gradient method to optimize a policy squared error criterion. On a parallel line of research, other authors have presented recently a gradient approximation of the maximum likelihood estimate of the reward signal. In general, both approaches approximate the gradient estimate and the criteria at different stages to make the algorithm tractable and efficient. In this work, we provide a detailed description of the different methods to highlight differences in terms of reward estimation, policy similarity and computational costs. We also provide experimental results to evaluate the differences in performance of the methods.
|
On the Performance of Maximum Likelihood Inverse Reinforcement Learning
| 2,286
|
We study upper and lower bounds on the sample-complexity of learning near-optimal behaviour in finite-state discounted Markov Decision Processes (MDPs). For the upper bound we make the assumption that each action leads to at most two possible next-states and prove a new bound for a UCRL-style algorithm on the number of time-steps when it is not Probably Approximately Correct (PAC). The new lower bound strengthens previous work by being both more general (it applies to all policies) and tighter. The upper and lower bounds match up to logarithmic factors.
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PAC Bounds for Discounted MDPs
| 2,287
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In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as a measure of its quality; our contribution is in the line of work which attempts to set up and study the statistical properties of new evaluation measures such as, e.g. ROC curves. In the confusion-based learning framework we propose, we claim that a targetted objective is to minimize the size of the confusion matrix C, measured through its operator norm ||C||. We derive generalization bounds on the (size of the) confusion matrix in an extended framework of uniform stability, adapted to the case of matrix valued loss. Pivotal to our study is a very recent matrix concentration inequality that generalizes McDiarmid's inequality. As an illustration of the relevance of our theoretical results, we show how two SVM learning procedures can be proved to be confusion-friendly. To the best of our knowledge, the present paper is the first that focuses on the confusion matrix from a theoretical point of view.
|
Confusion Matrix Stability Bounds for Multiclass Classification
| 2,288
|
In this paper, we study the application of GIST SVM in disease prediction (detection of cancer). Pattern classification problems can be effectively solved by Support vector machines. Here we propose a classifier which can differentiate patients having benign and malignant cancer cells. To improve the accuracy of classification, we propose to determine the optimal size of the training set and perform feature selection. To find the optimal size of the training set, different sizes of training sets are experimented and the one with highest classification rate is selected. The optimal features are selected through their F-Scores.
|
Application of Gist SVM in Cancer Detection
| 2,289
|
This work explores the effects of relevant and irrelevant boolean variables on the accuracy of classifiers. The analysis uses the assumption that the variables are conditionally independent given the class, and focuses on a natural family of learning algorithms for such sources when the relevant variables have a small advantage over random guessing. The main result is that algorithms relying predominately on irrelevant variables have error probabilities that quickly go to 0 in situations where algorithms that limit the use of irrelevant variables have errors bounded below by a positive constant. We also show that accurate learning is possible even when there are so few examples that one cannot determine with high confidence whether or not any individual variable is relevant.
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On the Necessity of Irrelevant Variables
| 2,290
|
Now-a-days the amount of data stored in educational database increasing rapidly. These databases contain hidden information for improvement of students' performance. Educational data mining is used to study the data available in the educational field and bring out the hidden knowledge from it. Classification methods like decision trees, Bayesian network etc can be applied on the educational data for predicting the student's performance in examination. This prediction will help to identify the weak students and help them to score better marks. The C4.5, ID3 and CART decision tree algorithms are applied on engineering student's data to predict their performance in the final exam. The outcome of the decision tree predicted the number of students who are likely to pass, fail or promoted to next year. The results provide steps to improve the performance of the students who were predicted to fail or promoted. After the declaration of the results in the final examination the marks obtained by the students are fed into the system and the results were analyzed for the next session. The comparative analysis of the results states that the prediction has helped the weaker students to improve and brought out betterment in the result.
|
Data Mining: A Prediction for Performance Improvement of Engineering
Students using Classification
| 2,291
|
We investigate adaptive mixture methods that linearly combine outputs of $m$ constituent filters running in parallel to model a desired signal. We use "Bregman divergences" and obtain certain multiplicative updates to train the linear combination weights under an affine constraint or without any constraints. We use unnormalized relative entropy and relative entropy to define two different Bregman divergences that produce an unnormalized exponentiated gradient update and a normalized exponentiated gradient update on the mixture weights, respectively. We then carry out the mean and the mean-square transient analysis of these adaptive algorithms when they are used to combine outputs of $m$ constituent filters. We illustrate the accuracy of our results and demonstrate the effectiveness of these updates for sparse mixture systems.
|
Adaptive Mixture Methods Based on Bregman Divergences
| 2,292
|
The past century was era of linear systems. Either systems (especially industrial ones) were simple (quasi)linear or linear approximations were accurate enough. In addition, just at the ending decades of the century profusion of computing devices were available, before then due to lack of computational resources it was not easy to evaluate available nonlinear system studies. At the moment both these two conditions changed, systems are highly complex and also pervasive amount of computation strength is cheap and easy to achieve. For recent era, a new branch of supervised learning well known as surrogate modeling (meta-modeling, surface modeling) has been devised which aimed at answering new needs of modeling realm. This short literature survey is on to introduce surrogate modeling to whom is familiar with the concepts of supervised learning. Necessity, challenges and visions of the topic are considered.
|
Very Short Literature Survey From Supervised Learning To Surrogate
Modeling
| 2,293
|
Bayesian model averaging (BMA) is an approach to average over alternative models; yet, it usually gets excessively concentrated around the single most probable model, therefore achieving only sub-optimal classification performance. The compression-based approach (Boulle, 2007) overcomes this problem, averaging over the different models by applying a logarithmic smoothing over the models' posterior probabilities. This approach has shown excellent performances when applied to ensembles of naive Bayes classifiers. AODE is another ensemble of models with high performance (Webb, 2005), based on a collection of non-naive classifiers (called SPODE) whose probabilistic predictions are aggregated by simple arithmetic mean. Aggregating the SPODEs via BMA rather than by arithmetic mean deteriorates the performance; instead, we aggregate the SPODEs via the compression coefficients and we show that the resulting classifier obtains a slight but consistent improvement over AODE. However, an important issue in any Bayesian ensemble of models is the arbitrariness in the choice of the prior over the models. We address this problem by the paradigm of credal classification, namely by substituting the unique prior with a set of priors. Credal classifier automatically recognize the prior-dependent instances, namely the instances whose most probable class varies, when different priors are considered; in these cases, credal classifiers remain reliable by returning a set of classes rather than a single class. We thus develop the credal version of both the BMA-based and the compression-based ensemble of SPODEs, substituting the single prior over the models by a set of priors. Experiments show that both credal classifiers provide higher classification reliability than their determinate counterparts; moreover the compression-based credal classifier compares favorably to previous credal classifiers.
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Credal Classification based on AODE and compression coefficients
| 2,294
|
We present a novel approach for training kernel Support Vector Machines, establish learning runtime guarantees for our method that are better then those of any other known kernelized SVM optimization approach, and show that our method works well in practice compared to existing alternatives.
|
The Kernelized Stochastic Batch Perceptron
| 2,295
|
Probabilistic generative modeling of data distributions can potentially exploit hidden information which is useful for discriminative classification. This observation has motivated the development of approaches that couple generative and discriminative models for classification. In this paper, we propose a new approach to couple generative and discriminative models in an unified framework based on PAC-Bayes risk theory. We first derive the model-parameter-independent stochastic feature mapping from a practical MAP classifier operating on generative models. Then we construct a linear stochastic classifier equipped with the feature mapping, and derive the explicit PAC-Bayes risk bounds for such classifier for both supervised and semi-supervised learning. Minimizing the risk bound, using an EM-like iterative procedure, results in a new posterior over hidden variables (E-step) and the update rules of model parameters (M-step). The derivation of the posterior is always feasible due to the way of equipping feature mapping and the explicit form of bounding risk. The derived posterior allows the tuning of generative models and subsequently the feature mappings for better classification. The derived update rules of the model parameters are same to those of the uncoupled models as the feature mapping is model-parameter-independent. Our experiments show that the coupling between data modeling generative model and the discriminative classifier via a stochastic feature mapping in this framework leads to a general classification tool with state-of-the-art performance.
|
Stochastic Feature Mapping for PAC-Bayes Classification
| 2,296
|
Nowadays, supervised learning is commonly used in many domains. Indeed, many works propose to learn new knowledge from examples that translate the expected behaviour of the considered system. A key issue of supervised learning concerns the description language used to represent the examples. In this paper, we propose a method to evaluate the feature set used to describe them. Our method is based on the computation of the consistency of the example base. We carried out a case study in the domain of geomatic in order to evaluate the sets of measures used to characterise geographic objects. The case study shows that our method allows to give relevant evaluations of measure sets.
|
Supervised feature evaluation by consistency analysis: application to
measure sets used to characterise geographic objects
| 2,297
|
Many studies on the cost-sensitive learning assumed that a unique cost matrix is known for a problem. However, this assumption may not hold for many real-world problems. For example, a classifier might need to be applied in several circumstances, each of which associates with a different cost matrix. Or, different human experts have different opinions about the costs for a given problem. Motivated by these facts, this study aims to seek the minimax classifier over multiple cost matrices. In summary, we theoretically proved that, no matter how many cost matrices are involved, the minimax problem can be tackled by solving a number of standard cost-sensitive problems and sub-problems that involve only two cost matrices. As a result, a general framework for achieving minimax classifier over multiple cost matrices is suggested and justified by preliminary empirical studies.
|
Minimax Classifier for Uncertain Costs
| 2,298
|
Multiple instance learning (MIL) has attracted great attention recently in machine learning community. However, most MIL algorithms are very slow and cannot be applied to large datasets. In this paper, we propose a greedy strategy to speed up the multiple instance learning process. Our contribution is two fold. First, we propose a density ratio model, and show that maximizing a density ratio function is the low bound of the DD model under certain conditions. Secondly, we make use of a histogram ratio between positive bags and negative bags to represent the density ratio function and find codebooks separately for positive bags and negative bags by a greedy strategy. For testing, we make use of a nearest neighbor strategy to classify new bags. We test our method on both small benchmark datasets and the large TRECVID MED11 dataset. The experimental results show that our method yields comparable accuracy to the current state of the art, while being up to at least one order of magnitude faster.
|
Greedy Multiple Instance Learning via Codebook Learning and Nearest
Neighbor Voting
| 2,299
|
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