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We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such as Gaussian and sparse sketching, using Johnson-Lindenstrauss embedding properties. We show that, when safeguarded with trust region or quadratic regularization, this random subspace approach satisfies, with high probability, a complexity bound of order $\mathcal{O}(\epsilon^{-2})$ to drive the (full) gradient below $\epsilon$; matching in the accuracy order, deterministic counterparts of these methods and securing almost sure convergence. Furthermore, no problem dimension dependence appears explicitly in the projection size of the sketching matrix, allowing the choice of low-dimensional subspaces. We particularise this framework to Random Subspace Gauss-Newton (RS-GN) methods for nonlinear least squares problems, that only require the calculation of the Jacobian in the subspace; with similar complexity guarantees. Numerical experiments with RS-GN on CUTEst nonlinear least squares are also presented, with some encouraging results., Comment: arXiv admin note: substantial text overlap with arXiv:2206.03371

We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection., Comment: This work first appears in Thirty-seventh International Conference on Machine Learning, 2020, in Workshop on Beyond First Order Methods in ML Systems. https://sites.google.com/view/optml-icml2020/accepted-papers?authuser=0. arXiv admin note: text overlap with arXiv:2206.03371

One of the key challenges in revenue management is unconstraining demand data. Existing state of the art single-class unconstraining methods make restrictive assumptions about the form of the underlying demand and can perform poorly when applied to data which breaks these assumptions. In this paper, we propose a novel unconstraining method that uses Gaussian process (GP) regression. We develop a novel GP model by constructing and implementing a new non-stationary covariance function for the GP which enables it to learn and extrapolate the underlying demand trend. We show that this method can cope with important features of realistic demand data, including nonlinear demand trends, variations in total demand, lengthy periods of constraining, non-exponential inter-arrival times, and discontinuities/changepoints in demand data. In all such circumstances, our results indicate that GPs outperform existing single-class unconstraining methods.

Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel subsequence interleaving model based on a probabilistic model of the sequence database, which allows us to search for the most compressing set of patterns without designing a specific encoding scheme. Our proposed algorithm is able to efficiently mine the most relevant sequential patterns and rank them using an associated measure of interestingness. The efficient inference in our model is a direct result of our use of a structural expectation-maximization framework, in which the expectation-step takes the form of a submodular optimization problem subject to a coverage constraint. We show on both synthetic and real world datasets that our model mines a set of sequential patterns with low spuriousness and redundancy, high interpretability and usefulness in real-world applications. Furthermore, we demonstrate that the quality of the patterns from our approach is comparable to, if not better than, existing state of the art sequential pattern mining algorithms., Comment: 10 pages in KDD 2016: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Existing API mining algorithms can be difficult to use as they require expensive parameter tuning and the returned set of API calls can be large, highly redundant and difficult to understand. To address this, we present PAM (Probabilistic API Miner), a near parameter-free probabilistic algorithm for mining the most interesting API call patterns. We show that PAM significantly outperforms both MAPO and UPMiner, achieving 69% test-set precision, at retrieving relevant API call sequences from GitHub. Moreover, we focus on libraries for which the developers have explicitly provided code examples, yielding over 300,000 LOC of hand-written API example code from the 967 client projects in the data set. This evaluation suggests that the hand-written examples actually have limited coverage of real API usages., Comment: 12 pages in FSE 2016: Proceedings of the 2016 24th ACM SIGSOFT International Symposium on Foundations of Software Engineering

Mining itemsets that are the most interesting under a statistical model of the underlying data is a commonly used and well-studied technique for exploratory data analysis, with the most recent interestingness models exhibiting state of the art performance. Continuing this highly promising line of work, we propose the first, to the best of our knowledge, generative model over itemsets, in the form of a Bayesian network, and an associated novel measure of interestingness. Our model is able to efficiently infer interesting itemsets directly from the transaction database using structural EM, in which the E-step employs the greedy approximation to weighted set cover. Our approach is theoretically simple, straightforward to implement, trivially parallelizable and retrieves itemsets whose quality is comparable to, if not better than, existing state of the art algorithms as we demonstrate on several real-world datasets., Comment: Supplementary material attached as Ancillary File; in PKDD 2016: European Conference on Machine Learning and Knowledge Discovery in Databases

Developers spend much of their time reading and browsing source code, raising new opportunities for summarization methods. Indeed, modern code editors provide code folding, which allows one to selectively hide blocks of code. However this is impractical to use as folding decisions must be made manually or based on simple rules. We introduce the autofolding problem, which is to automatically create a code summary by folding less informative code regions. We present a novel solution by formulating the problem as a sequence of AST folding decisions, leveraging a scoped topic model for code tokens. On an annotated set of popular open source projects, we show that our summarizer outperforms simpler baselines, yielding a 28% error reduction. Furthermore, we find through a case study that our summarizer is strongly preferred by experienced developers. More broadly, we hope this work will aid program comprehension by turning code folding into a usable and valuable tool., Comment: IEEE Transactions on Software Engineering 2017