There are three quite distinct ways to train a machine learning model on recommender system logs. The first method is to model the reward prediction for each possible recommendation to the user, at the scoring time the best recommendation is found by computing an argmax over the personalized recommendations. This method obeys principles such as the conditionality principle and the likelihood principle. A second method is useful when the model does not fit reality and underfits. In this case, we can use the fact that we know the distribution of historical recommendations (concentrated on previously identified good actions with some exploration) to adjust the errors in the fit to be evenly distributed over all actions. Finally, the inverse propensity score can be used to produce an estimate of the decision rules expected performance. The latter two methods violate the conditionality and likelihood principle but are shown to have good performance in certain settings. In this paper we review the literature around this fundamental, yet often overlooked choice and do some experiments using the RecoGym simulation environment.

Continual learning aims to enable machine learning models to learn a general solution space for past and future tasks in a sequential manner. Conventional models tend to forget the knowledge of previous tasks while learning a new task, a phenomenon known as catastrophic forgetting. When using Bayesian models in continual learning, knowledge from previous tasks can be retained in two ways: (i) posterior distributions over the parameters, containing the knowledge gained from inference in previous tasks, which then serve as the priors for the following task; (ii) coresets, containing knowledge of data distributions of previous tasks. Here, we show that Bayesian continual learning can be facilitated in terms of these two means through the use of natural gradients and Stein gradients respectively.

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model which can naturally incorporate a super-structure in order to reduce the set of possible candidate DAGs. We use the penalized negative log-likelihood score function with both $\ell_0$ and $\ell_1$ regularizations and propose a new mixed-integer quadratic optimization (MIQO) model, referred to as a layered network (LN) formulation. The LN formulation is a compact model, which enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only $\ell_1$ regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse super-structure.

Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent variable perspective. We first present a regularized recurrent attention filter for sensor fusion. This algorithm can dynamically combine information from different types of sensors in a sequential decision making task. Each sensor is bonded with a modular neural network to maximize utility of its own information. A gating modular neural network dynamically generates a set of mixing weights for outputs from sensor networks by balancing utility of all sensors' information. We design a co-learning mechanism to encourage co-adaption and independent learning of each sensor at the same time, and propose a regularization based co-learning method. In the second part, we focus on recovering the manifold of latent representation. We propose a co-learning approach using probabilistic graphical model which imposes a structural prior on the generative model: multimodal variational RNN (MVRNN) model, and derive a variational lower bound for its objective functions. In the third part, we extend the siamese structure to sensor fusion for robust acoustic event detection. We perform experiments to investigate the latent representations that are extracted; works will be done in the following months. Our experiments show that the recurrent attention filter can dynamically combine different sensor inputs according to the information carried in the inputs. We consider MVRNN can identify latent representations that are useful for many downstream tasks such as speech synthesis, activity recognition, and control and planning. Both algorithms are general frameworks which can be applied to other tasks where different types of sensors are jointly used for decision making.

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. Useful structured graphs include the multi-component graph, bipartite graph, connected graph, sparse graph, and regular graph. In general, structured graph learning is an NP-hard combinatorial problem, therefore, designing a general tractable optimization method is extremely challenging. In this paper, we introduce a unified graph learning framework lying at the integration of Gaussian graphical models and spectral graph theory. To impose a particular structure on a graph, we first show how to formulate the combinatorial constraints as an analytical property of the graph matrix. Then we develop an optimization framework that leverages graph learning with specific structures via spectral constraints on graph matrices. The proposed algorithms are provably convergent, computationally efficient, and practically amenable for numerous graph-based tasks. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. The code for all the simulations is made available as an open source repository.

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model, with the initial image serving as the latent variables, and discard the learned EBM. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. Moreover, unlike traditional EBM or MCMC, the learned short-run MCMC is also capable of reconstructing observed images and interpolating different images, like generator model or flow model. The code can be found in the Appendix.

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al., 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at \url{https://github.com/fishmoon1234/DAG-GNN}.

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter optimization are still hard and to a large extend open problems. In this paper, we consider the task of GP regression for time series modeling and analysis. The underlying stationary kernel can be approximated arbitrarily close by a new proposed grid spectral mixture (GSM) kernel, which turns out to be a linear combination of low-rank sub-kernels. In the case where a large number of the sub-kernels are used, either the Nystr\"{o}m or the random Fourier feature approximations can be adopted to deal efficiently with the computational demands. The unknown GP hyper-parameters consist of the non-negative weights of all sub-kernels as well as the noise variance; their estimation is performed via the maximum-likelihood (ML) estimation framework. Two efficient numerical optimization methods for solving the unknown hyper-parameters are derived, including a sequential majorization-minimization (MM) method and a non-linearly constrained alternating direction of multiplier method (ADMM). The MM matches perfectly with the proven low-rank property of the proposed GSM sub-kernels and turns out to be a part of efficiency, stable, and efficient solver, while the ADMM has the potential to generate better local minimum in terms of the test MSE. Experimental results, based on various classic time series data sets, corroborate that the proposed GSM kernel-based GP regression model outperforms several salient competitors of similar kind in terms of prediction mean-squared-error and numerical stability.

Research has provided evidence that associative classification produces more accurate results compared to other classification models. The Classification Based on Association (CBA) is one of the famous Associative Classification algorithms that generates accurate classifiers. However, current association classification algorithms reside external to databases, which reduces the flexibility of enterprise analytics systems. This paper implements the CBA in Oracle database using two variant models: hardcoding the CBA in Oracle Data Mining (ODM) package and Integrating Oracle Apriori model with the Oracle Decision tree model. We compared the proposed model performance with Naive Bayes, Support Vector Machine, Random Forests, and Decision Tree over 18 datasets from UCI. Results showed that our models outperformed the original CBA model with 1 percent and is competitive to chosen classification models over benchmark datasets.

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation algorithm, which updates the model variables layers by layers with the gradient descent algorithm or its variants. However, the objective functions of deep learning models to be optimized are usually non-convex and the gradient descent algorithms based on the first-order derivative can get stuck into the local optima very easily. To resolve such a problem, various local or global optimization algorithms have been proposed, which can help improve the training of deep learning models greatly. The representative examples include the Bayesian methods, Shubert-Piyavskii algorithm, Direct, LIPO, MCS, GA, SCE, DE, PSO, ES, CMA-ES, hill climbing and simulated annealing, etc. One part of these algorithms will be introduced in this paper (including the Bayesian method and Lipschitzian approaches, e.g., Shubert-Piyavskii algorithm, Direct, LIPO and MCS), and the remaining algorithms (including the population based optimization algorithms, e.g., GA, SCE, DE, PSO, ES and CMA-ES, and random search algorithms, e.g., hill climbing and simulated annealing) will be introduced in the follow-up paper [18] in detail.