We consider the problem of learning Markov Random Fields (including the prototypical example, the Ising model) under the constraint of differential privacy. Our learning goals include both structure learning, where we try to estimate the underlying graph structure of the model, as well as the harder goal of parameter learning, in which we additionally estimate the parameter on each edge. We provide algorithms and lower bounds for both problems under a variety of privacy constraints -- namely pure, concentrated, and approximate differential privacy. While non-privately, both learning goals enjoy roughly the same complexity, we show that this is not the case under differential privacy. In particular, only structure learning under approximate differential privacy maintains the non-private logarithmic dependence on the dimensionality of the data, while a change in either the learning goal or the privacy notion would necessitate a polynomial dependence. As a result, we show that the privacy constraint imposes a strong separation between these two learning problems in the high-dimensional data regime.

In some applications, acquiring covariates comes at a cost which is not negligible. For example in the medical domain, in order to classify whether a patient has diabetes or not, measuring glucose tolerance can be expensive. Assuming that the cost of each covariate, and the cost of misclassification can be specified by the user, our goal is to minimize the (expected) total cost of classification, i.e. the cost of misclassification plus the cost of the acquired covariates. We formalize this optimization goal using the (conditional) Bayes risk and describe the optimal solution using a recursive procedure. Since the procedure is computationally infeasible, we consequently introduce two assumptions: (1) the optimal classifier can be represented by a generalized additive model, (2) the optimal sets of covariates are limited to a sequence of sets of increasing size. We show that under these two assumptions, a computationally efficient solution exists. Furthermore, on several medical datasets, we show that the proposed method achieves in most situations the lowest total costs when compared to various previous methods. Finally, we weaken the requirement on the user to specify all misclassification costs by allowing the user to specify the minimally acceptable recall (target recall). Our experiments confirm that the proposed method achieves the target recall while minimizing the false discovery rate and the covariate acquisition costs better than previous methods.

Matrix factorization (MF) has been widely applied to collaborative filtering in recommendation systems. Its Bayesian variants can derive posterior distributions of user and item embeddings, and are more robust to sparse ratings. However, the Bayesian methods are restricted by their update rules for the posterior parameters due to the conjugacy of the priors and the likelihood. Neural networks can potentially address this issue by capturing complex mappings between the posterior parameters and the data. In this paper, we propose a variational auto-encoder based Bayesian MF framework. It leverages not only the data but also the information from the embeddings to approximate their joint posterior distribution. The approximation is an iterative procedure with cross feedback of user and item embeddings to the others' encoders. More specifically, user embeddings sampled in the previous iteration, alongside their ratings, are fed back into the item-side encoders to compute the posterior parameters for the item embeddings in the current iteration, and vice versa. The decoder network then reconstructs the data using the MF with the currently re-sampled user and item embeddings. We show the effectiveness of our framework in terms of reconstruction errors across five real-world datasets. We also perform ablation studies to illustrate the importance of the cross feedback component of our framework in lowering the reconstruction errors and accelerating the convergence.

Multinomial Logistic Regression is a well-studied tool for classification and has been widely used in fields like image processing, computer vision and, bioinformatics, to name a few. Under a supervised classification scenario, a Multinomial Logistic Regression model learns a weight vector to differentiate between any two classes by optimizing over the likelihood objective. With the advent of big data, the inundation of data has resulted in large dimensional weight vector and has also given rise to a huge number of classes, which makes the classical methods applicable for model estimation not computationally viable. To handle this issue, we here propose a parallel iterative algorithm: Parallel Iterative Algorithm for MultiNomial LOgistic Regression (PIANO) which is based on the Majorization Minimization procedure, and can parallely update each element of the weight vectors. Further, we also show that PIANO can be easily extended to solve the Sparse Multinomial Logistic Regression problem - an extensively studied problem because of its attractive feature selection property. In particular, we work out the extension of PIANO to solve the Sparse Multinomial Logistic Regression problem with l1 and l0 regularizations. We also prove that PIANO converges to a stationary point of the Multinomial and the Sparse Multinomial Logistic Regression problems. Simulations were conducted to compare PIANO with the existing methods, and it was found that the proposed algorithm performs better than the existing methods in terms of speed of convergence.

Obstructive sleep apnea (OSA), a form of sleep-disordered breathing characterized by recurrent episodes of partial or complete airway obstruction during sleep, is a serious health problem, affecting an estimated 1-5% of elementary school-aged children [9, 2]. Even mild forms of untreated pediatric OSA may cause high blood pressure, behavioral challenges, or impeded growth. Compared to adults, the symptoms of childhood-onset OSA are more varied and change continuously with development, making diagnosis a difficult challenge. The complexity of the data from surveys, biomedical measurements, 3D facial photos, and time-series data calls for state of the art techniques from mathematics and data science. Clinical data, including that considered in confirming or ruling out a diagnosis of pediatric OSA, consist of high-dimensional multi-mode data with mixtures of variables of disparate types (e.g., nominal and categorical data of different scales, interval data, time-to-event and longitudinal outcomes) also called mixed or noncommensurate data.

In this paper I argue that the search for explainable models and interpretable decisions in AI must be reformulated in terms of the broader project of offering a pragmatic and naturalistic account of understanding in AI. Intuitively, the purpose of providing an explanation of a model or a decision is to make it understandable to its stakeholders. But without a previous grasp of what it means to say that an agent understands a model or a decision, the explanatory strategies will lack a well-defined goal. Aside from providing a clearer objective for XAI, focusing on understanding also allows us to relax the factivity condition on explanation, which is impossible to fulfill in many machine learning models, and to focus instead on the pragmatic conditions that determine the best fit between a model and the methods and devices deployed to understand it. After an examination of the different types of understanding discussed in the philosophical and psychological literature, I conclude that interpretative or approximation models not only provide the best way to achieve the objectual understanding of a machine learning model, but are also a necessary condition to achieve post-hoc interpretability. This conclusion is partly based on the shortcomings of the purely functionalist approach to post-hoc interpretability that seems to be predominant in most recent literature.

The development of fair machine learning models that effectively avert bias and discrimination is an important problem that has garnered attention in recent years. The necessity of encoding complex relational dependencies among the features and variables for competent predictions require the development of fair, yet expressive relational models. In this work, we introduce Fair-A3SL, a fairness-aware structure learning algorithm for learning relational structures, which incorporates fairness measures while learning relational graphical model structures. Our approach is versatile in being able to encode a wide range of fairness metrics such as statistical parity difference, overestimation, equalized odds, and equal opportunity, including recently proposed relational fairness measures. While existing approaches employ the fairness measures on pre-determined model structures post prediction, Fair-A3SL directly learns the structure while optimizing for the fairness measures and hence is able to remove any structural bias in the model. We demonstrate the effectiveness of our learned model structures when compared with the state-of-the-art fairness models quantitatively and qualitatively on datasets representing three different modeling scenarios: i) a relational dataset, ii) a recidivism prediction dataset widely used in studying discrimination, and iii) a recommender systems dataset. Our results show that Fair-A3SL can learn fair, yet interpretable and expressive structures capable of making accurate predictions.

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference and learning efficiently on models that have very large treewidth. The highlight of the advance is that it works with standard (dense) factors, without the need for sparse factors or techniques based on knowledge compilation that are commonly utilized. This is significant as it permits a direct implementation of the improved variable elimination algorithm using tensors and their operations, leading to extremely efficient implementations especially when learning model parameters. Moreover, the proposed technique does not require knowledge of the specific functional dependencies, only that they exist, so can be used when learning these dependencies. We illustrate the efficacy of our proposed algorithm by compiling Bayesian network queries into tensor graphs and then learning their parameters from labeled data using a standard tool for tensor computation.

In this paper, we propose an approach for Facial Expressions Recognition (FER) based on a deep multi-facial patches aggregation network. Deep features are learned from facial patches using deep sub-networks and aggregated within one deep architecture for expression classification . Several problems may affect the performance of deep-learning based FER approaches, in particular, the small size of existing FER datasets which might not be sufficient to train large deep learning networks. Moreover, it is extremely time-consuming to collect and annotate a large number of facial images. To account for this, we propose two data augmentation techniques for facial expression generation to expand FER labeled training datasets. We evaluate the proposed framework on three FER datasets. Results show that the proposed approach achieves state-of-art FER deep learning approaches performance when the model is trained and tested on images from the same dataset. Moreover, the proposed data augmentation techniques improve the expression recognition rate, and thus can be a solution for training deep learning FER models using small datasets. The accuracy degrades significantly when testing for dataset bias.

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational) DGPs, including mini-batch training and predictive uncertainty that is controlled by kernel basis functions. Importantly, since DSPPs admit a simple maximum likelihood inference procedure, the resulting predictive distributions are not degraded by any posterior approximations. In an extensive empirical comparison on univariate and multivariate regression tasks we find that the resulting predictive distributions are significantly better calibrated than those obtained with other probabilistic methods for scalable regression, including variational DGPs--often by as much as a nat per datapoint.