Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters of a wide variety of machine learning models. The success of machine learning has led practitioners in diverse real-world settings to learn classifiers for practical problems. As machine learning becomes commonplace, Bayesian optimization becomes an attractive method for practitioners to automate the process of classifier hyper-parameter tuning. A key observation is that the data used for tuning models in these settings is often sensitive. Certain data such as genetic predisposition, personal email statistics, and car accident history, if not properly private, may be at risk of being inferred from Bayesian optimization outputs. To address this, we introduce methods for releasing the best hyper-parameters and classifier accuracy privately. Leveraging the strong theoretical guarantees of differential privacy and known Bayesian optimization convergence bounds, we prove that under a GP assumption these private quantities are also near-optimal. Finally, even if this assumption is not satisfied, we can use different smoothness guarantees to protect privacy.

A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via deconvolutional inference. To speed up this inference, a new statistical approach is proposed to project the top-layer dictionary elements to the data level. Following this, only one layer of deconvolution is required during testing. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images. Excellent classification results are obtained on both the MNIST and Caltech 101 datasets.

This paper uses natural language processing to create the first machine-coded democracy index, which I call Automated Democracy Scores (ADS). The ADS are based on 42 million news articles from 6,043 different sources and cover all independent countries in the 1993-2012 period. Unlike the democracy indices we have today the ADS are replicable and have standard errors small enough to actually distinguish between cases. The ADS are produced with supervised learning. Three approaches are tried: a) a combination of Latent Semantic Analysis and tree-based regression methods; b) a combination of Latent Dirichlet Allocation and tree-based regression methods; and c) the Wordscores algorithm. The Wordscores algorithm outperforms the alternatives, so it is the one on which the ADS are based. There is a web application where anyone can change the training set and see how the results change: democracy-scores.org

In this paper, we develop a method for unsupervised clustering of two-way (matrix) data by combining two recent innovations from different fields: the Sparse Subspace Clustering (SSC) algorithm [10], which groups points coming from a union of subspaces into their respective subspaces, and the t-product [18], which was introduced to provide a matrix-like multiplication for third order tensors. Our algorithm is analogous to SSC in that an "affinity" between different data points is built using a sparse self-representation of the data. Unlike SSC, we employ the t-product in the self-representation. This allows us more flexibility in modeling; infact, SSC is a special case of our method. When using the t-product, three-way arrays are treated as matrices whose elements (scalars) are n-tuples or tubes. Convolutions take the place of scalar multiplication. This framework allows us to embed the 2-D data into a vector-space-like structure called a free module over a commutative ring. These free modules retain many properties of complex inner-product spaces, and we leverage that to provide theoretical guarantees on our algorithm. We show that compared to vector-space counterparts, SSmC achieves higher accuracy and better able to cluster data with less preprocessing in some image clustering problems. In particular we show the performance of the proposed method on Weizmann face database, the Extended Yale B Face database and the MNIST handwritten digits database.

In this paper, we focus on developing efficient sensitivity analysis methods for a computationally expensive objective function $f(x)$ in the case that the minimization of it has just been performed. Here "computationally expensive" means that each of its evaluation takes significant amount of time, and therefore our main goal to use a small number of function evaluations of $f(x)$ to further infer the sensitivity information of these different parameters. Correspondingly, we consider the optimization procedure as an adaptive experimental design and re-use its available function evaluations as the initial design points to establish a surrogate model $s(x)$ (or called response surface). The sensitivity analysis is performed on $s(x)$, which is an lieu of $f(x)$. Furthermore, we propose a new local multivariate sensitivity measure, for example, around the optimal solution, for high dimensional problems. Then a corresponding "objective-oriented experimental design" is proposed in order to make the generated surrogate $s(x)$ better suitable for the accurate calculation of the proposed specific local sensitivity quantities. In addition, we demonstrate the better performance of the Gaussian radial basis function interpolator over Kriging in our cases, which are of relatively high dimensionality and few experimental design points. Numerical experiments demonstrate that the optimization procedure and the "objective-oriented experimental design" behavior much better than the classical Latin Hypercube Design. In addition, the performance of Kriging is not as good as Gaussian RBF, especially in the case of high dimensional problems.

Recently, fully-connected and convolutional neural networks have been trained to achieve state-of-the-art performance on a wide variety of tasks such as speech recognition, image classification, natural language processing, and bioinformatics. For classification tasks, most of these "deep learning" models employ the softmax activation function for prediction and minimize cross-entropy loss. In this paper, we demonstrate a small but consistent advantage of replacing the softmax layer with a linear support vector machine. Learning minimizes a margin-based loss instead of the cross-entropy loss. While there have been various combinations of neural nets and SVMs in prior art, our results using L2-SVMs show that by simply replacing softmax with linear SVMs gives significant gains on popular deep learning datasets MNIST, CIFAR-10, and the ICML 2013 Representation Learning Workshop's face expression recognition challenge.

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs and implemented these heuristics in systems for decision theoretic planning. In this paper, we study the complexity of the computational problems addressed by such implementations. In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization placing these problems within the polynomial hierarchy. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for $\Sigma_k$ formulas, and for corresponding GFODDs, evaluation and satisfiability are $\Sigma_k^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete. For $\Pi_k$ formulas evaluation is $\Pi_k^p$ complete, satisfiability is one level higher and is $\Sigma_{k+1}^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete.

MILJS is a collection of state-of-the-art, platform-independent, scalable, fast JavaScript libraries for matrix calculation and machine learning. Our core library offering a matrix calculation is called Sushi, which exhibits far better performance than any other leading machine learning libraries written in JavaScript. Especially, our matrix multiplication is 177 times faster than the fastest JavaScript benchmark. Based on Sushi, a machine learning library called Tempura is provided, which supports various algorithms widely used in machine learning research. We also provide Soba as a visualization library. The implementations of our libraries are clearly written, properly documented and thus can are easy to get started with, as long as there is a web browser. These libraries are available from http://mil-tokyo.github.io/

We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to minimize prediction error for a user-specified {\it average} feature acquisition budget. While random forests yield strong generalization performance, they do not explicitly account for feature costs and furthermore require low correlation among trees, which amplifies costs. Our random forest grows trees with low acquisition cost and high strength based on greedy minimax cost-weighted-impurity splits. Theoretically, we establish near-optimal acquisition cost guarantees for our algorithm. Empirically, on a number of benchmark datasets we demonstrate superior accuracy-cost curves against state-of-the-art prediction-time algorithms.

The earliest reference to principal components analysis (PCA) is in [14]. Since then, PCA has evolved into a classic tool for data analysis. A challenge for the interpretation of the principal components (or factors) is that they can be linear combinations of all the original variables. When the original variables have direct physical significance (e.g.