We consider the optimal value of information (VoI) problem, where the goal is to sequentially select a set of tests with a minimal cost, so that one can efficiently make the best decision based on the observed outcomes. Existing algorithms are either heuristics with no guarantees, or scale poorly (with exponential run time in terms of the number of available tests). Moreover, these methods assume a known distribution over the test outcomes, which is often not the case in practice. We propose an efficient sampling-based online learning framework to address the above issues. First, assuming the distribution over hypotheses is known, we propose a dynamic hypothesis enumeration strategy, which allows efficient information gathering with strong theoretical guarantees. We show that with sufficient amount of samples, one can identify a near-optimal decision with high probability. Second, when the parameters of the hypotheses distribution are unknown, we propose an algorithm which learns the parameters progressively via posterior sampling in an online fashion. We further establish a rigorous bound on the expected regret. We demonstrate the effectiveness of our approach on a real-world interactive troubleshooting application and show that one can efficiently make high-quality decisions with low cost.

Let me know what you think @StephLKim.

Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as powerful frameworks for deep generative model learning, have largely been considered as two distinct paradigms and received extensive independent study respectively. This paper establishes formal connections between deep generative modeling approaches through a new formulation of GANs and VAEs. We show that GANs and VAEs are essentially minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to exchange ideas across research lines in a principled way. For example, we transfer the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism for leveraging generated samples. Quantitative experiments show generality and effectiveness of the imported extensions.

The machine learning community adopted the use of null hypothesis significance testing (NHST) in order to ensure the statistical validity of results. Many scientific fields however realized the shortcomings of frequentist reasoning and in the most radical cases even banned its use in publications. We should do the same: just as we have embraced the Bayesian paradigm in the development of new machine learning methods, so we should also use it in the analysis of our own results. We argue for abandonment of NHST by exposing its fallacies and, more importantly, offer better - more sound and useful - alternatives for it.

Use neighborhood component analysis (NCA) to choose features for machine learning models. Manipulate and analyze data that is too big to fit in memory. Perform support vector machine (SVM) and Naive Bayes classification, create bags of decision trees, and fit lasso regression on out-of-memory data. Process big data with tall arrays in parallel on your desktop, MATLAB Distributed Computing Server, and Spark clusters. Manipulate, compare, and store text data efficiently .

The problem of learning structural equation models (SEMs) from data is a fundamental problem in causal inference. We develop a new algorithm --- which is computationally and statistically efficient and works in the high-dimensional regime --- for learning linear SEMs from purely observational data with arbitrary noise distribution. We consider three aspects of the problem: identifiability, computational efficiency, and statistical efficiency. We show that when data is generated from a linear SEM over $p$ nodes and maximum degree $d$, our algorithm recovers the directed acyclic graph (DAG) structure of the SEM under an identifiability condition that is more general than those considered in the literature, and without faithfulness assumptions. In the population setting, our algorithm recovers the DAG structure in $\mathcal{O}(p(d^2 + \log p))$ operations. In the finite sample setting, if the estimated precision matrix is sparse, our algorithm has a smoothed complexity of $\widetilde{\mathcal{O}}(p^3 + pd^7)$, while if the estimated precision matrix is dense, our algorithm has a smoothed complexity of $\widetilde{\mathcal{O}}(p^5)$. For sub-Gaussian noise, we show that our algorithm has a sample complexity of $\mathcal{O}(\frac{d^8}{\varepsilon^2} \log (\frac{p}{\sqrt{\delta}}))$ to achieve $\varepsilon$ element-wise additive error with respect to the true autoregression matrix with probability at most $1 - \delta$, while for noise with bounded $(4m)$-th moment, with $m$ being a positive integer, our algorithm has a sample complexity of $\mathcal{O}(\frac{d^8}{\varepsilon^2} (\frac{p^2}{\delta})^{1/m})$.

The Word2Vec model has become a standard method for representing words as dense vectors. This is typically done as a preprocessing step, after which the learned vectors are fed into a discriminative model (typically an RNN) to generate predictions such as movie review sentiment, do machine translation, or even generate text, character by character. Previously, the bag of words model was commonly used to represent words and sentences as numerical vectors, which could then be fed into a classifier (for example Naive Bayes) to produce output predictions. Given a vocabulary of words and a document of words, a -dimensional vector would be created to represent the vector, where index denotes the number of times the th word in the vocabulary occured in the document. This model represented words as atomic units, assuming that all words were independent of each other.

In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real-world datasets. Furthermore, we extend the models with the Bayesian automatic relevance determination prior, allowing the models to perform automatic model selection, and demonstrate its efficiency.

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages.

We study a two-level multiview learning with more than two views under the PAC-Bayesian framework. This approach, sometimes referred as late fusion, consists in learning sequentially multiple view-specific classifiers at the first level, and then combining these view-specific classifiers at the second level. Our main theoretical result is a generalization bound on the risk of the majority vote which exhibits a term of diversity in the predictions of the view-specific classifiers. From this result it comes out that controlling the trade-off between diversity and accuracy is a key element for multiview learning, which complements other results in multiview learning. Finally, we experiment our principle on multiview datasets extracted from the Reuters RCV1/RCV2 collection.