Inverse classification is the process of manipulating an instance such that it is more likely to conform to a specific class. Past methods that address such a problem have shortcomings. Greedy methods make changes that are overly radical, often relying on data that is strictly discrete. Other methods rely on certain data points, the presence of which cannot be guaranteed. In this paper we propose a general framework and method that overcomes these and other limitations. The formulation of our method uses any differentiable classification function. We demonstrate the method by using Gaussian kernel SVMs. We constrain the inverse classification to occur on features that can actually be changed, each of which incurs an individual cost. We further subject such changes to fall within a certain level of cumulative change (budget). Our framework can also accommodate the estimation of features whose values change as a consequence of actions taken (indirectly changeable features). Furthermore, we propose two methods for specifying feature-value ranges that result in different algorithmic behavior. We apply our method, and a proposed sensitivity analysis-based benchmark method, to two freely available datasets: Student Performance, from the UCI Machine Learning Repository and a real-world cardiovascular disease dataset. The results obtained demonstrate the validity and benefits of our framework and method.
Algorithmic data types, which refers to the type of data a particular optimization algorithm has the capability of operating on, also fall into two categories: @cite_11 @cite_23 @cite_5 and @cite_2 @cite_7 @cite_4 . Discrete data types lead to coarse-grained recommendations, while continuous data types provide those that are more fine-grained. In this work, we focus on the latter, as precision recommendations are the goal.
@cite_4 @cite_7 @cite_23 @cite_2 @cite_5 @cite_11
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type="main" xml:id="insr12022-abs-0001"> Modern computational statistics is turning more and more to high-dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include non-differentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well-chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience. Data sets are often modeled as samples from a probability distribution in RD, for D large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a d-dimensional manifold M, with d much smaller than D. When M is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of d vectors in RD (for example found by SVD), at a cost (n+D)d for n data points. When M is nonlinear, there are no “explicit” and algorithmically efficient constructions of dictionaries that achieve a similar efficiency: typically one uses either random dictionaries, or dictionaries obtained by black-box global optimization. In this paper we construct data-dependent multi-scale dictionaries that aim at efficiently encoding and manipulating the data. Their construction is fast, and so are the algorithms that map data points to dictionary coefficients and vice versa, in contrast with L1-type sparsity-seeking algorithms, but like adaptive nonlinear approximation in classical multi-scale analysis. In addition, data points are guaranteed to have a compressible representation in terms of the dictionary, depending on the assumptions on the geometry of the underlying probability distribution. Many recommendation algorithms suffer from popularity bias in their output: popular items are recommended frequently and less popular ones rarely, if at all. However, less popular, long-tail items are precisely those that are often desirable recommendations. In this paper, we introduce a flexible regularization-based framework to enhance the long-tail coverage of recommendation lists in a learning-to-rank algorithm. We show that regularization provides a tunable mechanism for controlling the trade-off between accuracy and coverage. Moreover, the experimental results using two data sets show that it is possible to improve coverage of long tail items without substantial loss of ranking performance. We present in this paper first-order alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most @math iterations to obtain an @math -optimal solution, while our accelerated (i.e., fast) versions of them require at most @math iterations, with little change in the computational effort required at each iteration. For both types of methods, we present one algorithm that requires both functions to be smooth with Lipschitz continuous gradients and one algorithm that needs only one of the functions to be so. Algorithms in this paper are Gauss-Seidel type methods, in contrast to the ones proposed by Goldfarb and Ma in [21] where the algorithms are Jacobi type methods. Numerical results are reported to support our theoretical conclusions and demonstrate the practical potential of our algorithms. Users may strive to formulate an adequate textual query for their information need. Search engines assist the users by presenting query suggestions. To preserve the original search intent, suggestions should be context-aware and account for the previous queries issued by the user. Achieving context awareness is challenging due to data sparsity. We present a novel hierarchical recurrent encoder-decoder architecture that makes possible to account for sequences of previous queries of arbitrary lengths. As a result, our suggestions are sensitive to the order of queries in the context while avoiding data sparsity. Additionally, our model can suggest for rare, or long-tail, queries. The produced suggestions are synthetic and are sampled one word at a time, using computationally cheap decoding techniques. This is in contrast to current synthetic suggestion models relying upon machine learning pipelines and hand-engineered feature sets. Results show that our model outperforms existing context-aware approaches in a next query prediction setting. In addition to query suggestion, our architecture is general enough to be used in a variety of other applications. Decision rules, which can provide good interpretability and flexibility for data mining tasks, have received very little attention in the stream mining community so far. In this work we introduce a new algorithm to learn rule sets, designed for open-ended data streams. The proposed algorithm is able to continuously learn compact ordered and unordered rule sets. The experimental evaluation shows competitive results in comparison with VFDT and C4.5rules. Mining discrete patterns in binary data is important for subsampling, compression, and clustering. We consider rank-one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds. Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under that attribute, sorted by grade (highest grade first). Each object is assigned an overall grade, that is obtained by combining the attribute grades using a fixed monotone aggregation function, or combining rule, such as min or average. To determine the top k objects, that is, k objects with the highest overall grades, the naive algorithm must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm ("Fagin's Algorithm", or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably simple algorithm ("the threshold algorithm", or TA) that is optimal in a much stronger sense than FA. We show that TA is essentially optimal, not just for some monotone aggregation functions, but for all of them, and not just in a high-probability worst-case sense, but over every database. Unlike FA, which requires large buffers (whose size may grow unboundedly as the database size grows), TA requires only a small, constant-size buffer. TA allows early stopping, which yields, in a precise sense, an approximate version of the top k answers. We distinguish two types of access: sorted access (where the middleware system obtains the grade of an object in some sorted list by proceeding through the list sequentially from the top), and random access (where the middleware system requests the grade of object in a list, and obtains it in one step). We consider the scenarios where random access is either impossible, or expensive relative to sorted access, and provide algorithms that are essentially optimal for these cases as well. Abstract Recently, incremental and on-line learning gained more attention especially in the context of big data and learning from data streams, conflicting with the traditional assumption of complete data availability. Even though a variety of different methods are available, it often remains unclear which of them is suitable for a specific task and how they perform in comparison to each other. We analyze the key properties of eight popular incremental methods representing different algorithm classes. Thereby, we evaluate them with regards to their on-line classification error as well as to their behavior in the limit. Further, we discuss the often neglected issue of hyperparameter optimization specifically for each method and test how robustly it can be done based on a small set of examples. Our extensive evaluation on data sets with different characteristics gives an overview of the performance with respect to accuracy, convergence speed as well as model complexity, facilitating the choice of the best method for a given application. We introduce a novel algorithmic approach to content recommendation based on adaptive clustering of exploration-exploitation "bandit") strategies. We provide a sharp regret analysis of this algorithm in a standard stochastic noise setting, demonstrate its scalability properties, and prove its effectiveness on a number of artificial and real-world datasets. Our experiments show a significant increase in prediction performance over state-of-the-art methods for bandit problems. In this paper, we address the problem of searching for semantically similar images from a large database. We present a compact coding approach, supervised quantization. Our approach simultaneously learns feature selection that linearly transforms the database points into a low-dimensional discriminative subspace, and quantizes the data points in the transformed space. The optimization criterion is that the quantized points not only approximate the transformed points accurately, but also are semantically separable: the points belonging to a class lie in a cluster that is not overlapped with other clusters corresponding to other classes, which is formulated as a classification problem. The experiments on several standard datasets show the superiority of our approach over the state-of-the art supervised hashing and unsupervised quantization algorithms. In this study, we examine the use of graph ordering algorithms for visual analysis of data sets using visual similarity matrices. Visual similarity matrices display the relationships between data items in a dot-matrix plot format, with the axes labeled with the data items and points drawn if there is a relationship between two data items. The biggest challenge for displaying data using this representation is finding an ordering of the data items that reveals the internal structure of the data set. Poor orderings are indistinguishable from noise whereas a good ordering can reveal complex and subtle features of the data. We consider three general classes of algorithms for generating orderings: simple graph theoretic algorithms, symbolic sparse matrix reordering algorithms, and spectral decomposition algorithms. We apply each algorithm to synthetic and real world data sets and evaluate each algorithm for interpretability (i.e., does the algorithm lead to images with usable visual features?) and stability (i.e., does the algorithm consistently produce similar results?). We also provide a detailed discussion of the results for each algorithm across the different graph types and include a discussion of some strategies for using ordering algorithms for data analysis based on these results. The application of frequent patterns in classification appeared in sporadic studies and achieved initial success in the classification of relational data, text documents and graphs. In this paper, we conduct a systematic exploration of frequent pattern-based classification, and provide solid reasons supporting this methodology. It was well known that feature combinations (patterns) could capture more underlying semantics than single features. However, inclusion of infrequent patterns may not significantly improve the accuracy due to their limited predictive power. By building a connection between pattern frequency and discriminative measures such as information gain and Fisher score, we develop a strategy to set minimum support in frequent pattern mining for generating useful patterns. Based on this strategy, coupled with a proposed feature selection algorithm, discriminative frequent patterns can be generated for building high quality classifiers. We demonstrate that the frequent pattern-based classification framework can achieve good scalability and high accuracy in classifying large datasets. Empirical studies indicate that significant improvement in classification accuracy is achieved (up to 12 in UCI datasets) using the so-selected discriminative frequent patterns. Users may strive to formulate an adequate textual query for their information need. Search engines assist the users by presenting query suggestions. To preserve the original search intent, suggestions should be context-aware and account for the previous queries issued by the user. Achieving context awareness is challenging due to data sparsity. We present a probabilistic suggestion model that is able to account for sequences of previous queries of arbitrary lengths. Our novel hierarchical recurrent encoder-decoder architecture allows the model to be sensitive to the order of queries in the context while avoiding data sparsity. Additionally, our model can suggest for rare, or long-tail, queries. The produced suggestions are synthetic and are sampled one word at a time, using computationally cheap decoding techniques. This is in contrast to current synthetic suggestion models relying upon machine learning pipelines and hand-engineered feature sets. Results show that it outperforms existing context-aware approaches in a next query prediction setting. In addition to query suggestion, our model is general enough to be used in a variety of other applications. We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization, or sized types bound the resource usage or result size of such a procedure by a sum of unary functions of the sizes of the arguments. In this paper we generalize this to arbitrary multivariate polynomial functions thus allowing bounds of the form mn which had to be grossly overestimated by m2+n2 before. Our framework even encompasses bounds like ∗i,j≤n m_i mj where the mi are the sizes of the entries of a list of length n. This allows us for the first time to derive useful resource bounds for operations on matrices that are represented as lists of lists and to considerably improve bounds on other super-linear operations on lists such as longest common subsequence and removal of duplicates from lists of lists. Furthermore, resource bounds are now closed under composition which improves accuracy of the analysis of composed programs when some or all of the components exhibit super-linear resource or size behavior. The analysis is based on a novel multivariate amortized resource analysis. We present it in form of a type system for a simple first-order functional language with lists and trees, prove soundness, and describe automatic type inference based on linear programming. We have experimentally validated the automatic analysis on a wide range of examples from functional programming with lists and trees. The obtained bounds were compared with actual resource consumption. All bounds were asymptotically tight, and the constants were close or even identical to the optimal ones. This paper focuses on developing effective and efficient algorithms for top-N recommender systems. A novel Sparse Linear Method (SLIM) is proposed, which generates top-N recommendations by aggregating from user purchase rating profiles. A sparse aggregation coefficient matrix W is learned from SLIM by solving an 1-norm and 2-norm regularized optimization problem. W is demonstrated to produce high quality recommendations and its sparsity allows SLIM to generate recommendations very fast. A comprehensive set of experiments is conducted by comparing the SLIM method and other state-of-the-art top-N recommendation methods. The experiments show that SLIM achieves significant improvements both in run time performance and recommendation quality over the best existing methods. There is growing interest in algorithms for processing and querying continuous data streams (i.e., data seen only once in a fixed order) with limited memory resources. In its most general form, a data stream is actually an update stream, i.e., comprising data-item deletions as well as insertions. Such massive update streams arise naturally in several application domains (e.g., monitoring of large IP network installations or processing of retail-chain transactions). Estimating the cardinality of set expressions defined over several (possibly distributed) update streams is perhaps one of the most fundamental query classes of interest; as an example, such a query may ask “what is the number of distinct IP source addresses seen in passing packets from both router R1 and R 2 but not router R3?”. Earlier work only addressed very restricted forms of this problem, focusing solely on the special case of insert-only streams and specific operators (e.g., union). In this paper, we propose the first space-efficient algorithmic solution for estimating the cardinality of full-fledged set expressions over general update streams. Our estimation algorithms are probabilistic in nature and rely on a novel, hash-based synopsis data structure, termed ”2-level hash sketch”. We demonstrate how our 2-level hash sketch synopses can be used to provide low-error, high-confidence estimates for the cardinality of set expressions (including operators such as set union, intersection, and difference) over continuous update streams, using only space that is significantly sublinear in the sizes of the streaming input (multi-)sets. Furthermore, our estimators never require rescanning or resampling of past stream items, regardless of the number of deletions in the stream. We also present lower bounds for the problem, demonstrating that the space usage of our estimation algorithms is within small factors of the optimal. Finally, we propose an optimized, time-efficient stream synopsis (based on 2-level hash sketches) that provides similar, strong accuracy-space guarantees while requiring only guaranteed logarithmic maintenance time per update, thus making our methods applicable for truly rapid-rate data streams. Our results from an empirical study of our synopsis and estimation techniques verify the effectiveness of our approach. The goal of personalized history-based recommendation is to automatically output a distribution over all the items given a sequence of previous purchases of a user. In this work, we present a novel approach that uses a recurrent network for summarizing the history of purchases, continuous vectors representing items for scalability, and a novel attention-based recurrent mixture density network, which outputs each component in a mixture sequentially, for modelling a multi-modal conditional distribution. We evaluate the proposed approach on two publicly available datasets, MovieLens-20M and RecSys15. The experiments show that the proposed approach, which explicitly models the multi-modal nature of the predictive distribution, is able to improve the performance over various baselines in terms of precision, recall and nDCG. In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower bounds for private ERM assuming only that each data point's contribution to the loss function is Lipschitz bounded and that the domain of optimization is bounded. We provide a separate set of algorithms and matching lower bounds for the setting in which the loss functions are known to also be strongly convex. Our algorithms run in polynomial time, and in some cases even match the optimal non-private running time (as measured by oracle complexity). We give separate algorithms (and lower bounds) for @math - and @math -differential privacy; perhaps surprisingly, the techniques used for designing optimal algorithms in the two cases are completely different. Our lower bounds apply even to very simple, smooth function families, such as linear and quadratic functions. This implies that algorithms from previous work can be used to obtain optimal error rates, under the additional assumption that the contributions of each data point to the loss function is smooth. We show that simple approaches to smoothing arbitrary loss functions (in order to apply previous techniques) do not yield optimal error rates. In particular, optimal algorithms were not previously known for problems such as training support vector machines and the high-dimensional median. We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly convergent algorithms for this class of problems which are common in machine learning. While the algorithmic extension is straightforward, it comes with challenges and opportunities: (a) the convex minimization analysis does not apply and we use the notion of monotone operators to prove convergence, showing in particular that the same algorithm applies to a larger class of problems, such as variational inequalities, (b) there are two notions of splits, in terms of functions, or in terms of partial derivatives, (c) the split does need to be done with convex-concave terms, (d) non-uniform sampling is key to an efficient algorithm, both in theory and practice, and (e) these incremental algorithms can be easily accelerated using a simple extension of the "catalyst" framework, leading to an algorithm which is always superior to accelerated batch algorithms.