Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approach: first, we transform this task into a constrained matrix completion problem with entries bounded in the unit interval [0, 1]; second, we propose two novel matrix factorization models that leverage our knowledge of the VFX environment. Our first approach, expertise matrix factorization (EMF), is an interpretable method that structures the latent factors as weighted user-item interplay. The second one, survival matrix factorization (SMF), is instead a probabilistic model for the underlying process defining employees' efficiencies. We show the effectiveness of our proposed models by extensive numerical tests on our VFX dataset and two additional datasets with values that are also bounded in the [0, 1] interval.

In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many candidates as they wish. Winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most votes. An agent may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics to strategize, instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in multi-winner approval voting scenarios with complete information. We show that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. Instead, voters tend to prioritize the candidates with the highest utilities. Using simulations, we demonstrate the effectiveness of these heuristics in situations where agents only have access to partial information.

It seems to be a pearl of conventional wisdom that parameter learning in deep sum-product networks is surprisingly fast compared to shallow mixture models. This paper examines the effects of overparameterization in sum-product networks on the speed of parameter optimisation. Using theoretical analysis and empirical experiments, we show that deep sum-product networks exhibit an implicit acceleration compared to their shallow counterpart. In fact, gradient-based optimisation in deep tree-structured sum-product networks is equal to gradient ascend with adaptive and time-varying learning rates and additional momentum terms.

Probabilistic approach to Boolean matrix factorization can provide solutions robust against noise and missing values with linear computational complexity. However, the assumption about latent factors can be problematic in real world applications. This study proposed a new probabilistic algorithm free of assumptions of latent factors, while retaining the advantages of previous algorithms. Real data experiment showed that our algorithm was favourably compared with current state-of-the-art probabilistic algorithms.

Directed graphical models (DGMs) are a class of probabilistic models that are widely used for predictive analysis in sensitive domains, such as medical diagnostics. In this paper we present an algorithm for differentially private learning of the parameters of a DGM with a publicly known graph structure over fully observed data. Our solution optimizes for the utility of inference queries over the DGM and \textit{adds noise that is customized to the properties of the private input dataset and the graph structure of the DGM}. To the best of our knowledge, this is the first explicit data-dependent privacy budget allocation algorithm for DGMs. We compare our algorithm with a standard data-independent approach over a diverse suite of DGM benchmarks and demonstrate that our solution requires a privacy budget that is $3\times$ smaller to obtain the same or higher utility.

Several structure learning algorithms have been proposed towards discovering causal or Bayesian Network (BN) graphs, which is a particularly challenging problem in AI. The performance of these algorithms is evaluated based on the relationship the learned graph has with respect to the ground truth graph. However, there is no agreed scoring function to determine this relationship. Moreover, this paper shows that the commonly used metrics tend to be biased in favour of graphs that minimise the number of edges. The evaluation bias is inconsistent and may lead to evaluating graphs with no edges as superior to graphs with varying numbers of correct and incorrect edges; implying that graphs that minimise edges are often favoured over more complex graphs due to bias rather than overall accuracy. While graphs that are less complex are often desirable, the current metrics encourage algorithms to optimise for simplicity, and to discover graphs with a limited number of edges that do not enable full propagation of evidence. This paper proposes a Balanced Scoring Function (BSF) that eliminates this bias by adjusting the reward function based on the difficulty of discovering an edge, or no edge, proportional to their occurrence rate in the ground truth graph. The BSF score can be used in conjunction with other traditional metrics to provide an alternative and unbiased assessment about the capability of structure learning algorithms in discovering causal or BN graphs.

Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured, nonparametric edge-exchangeable graphs. However, such exchangeable models necessarily ignore temporal dynamics in the network. We propose a dynamic nonparametric model for interaction graphs that combine the sparsity of the exchangeable models with dynamic clustering patterns that tend to reinforce recent behavioral patterns. We show that our method yields improved held-out likelihood over stationary variants, and impressive predictive performance against a range of state-of-the-art dynamic interaction graph models.

Deep Neural Networks (DNNs) often rely on very large datasets for training. Given the large size of such datasets, it is conceivable that they contain certain samples that either do not contribute or negatively impact the DNN's performance. If there is a large number of such samples, subsampling the training dataset in a way that removes them could provide an effective solution to both improve performance and reduce training time. In this paper, we propose an approach called Active Dataset Subsampling (ADS), to identify favorable subsets within a dataset for training using ensemble based uncertainty estimation. When applied to three image classification benchmarks (CIFAR-10, CIFAR-100 and ImageNet) we find that there are low uncertainty subsets, which can be as large as 50% of the full dataset, that negatively impact performance. These subsets are identified and removed with ADS. We demonstrate that datasets obtained using ADS with a lightweight ResNet-18 ensemble remain effective when used to train deeper models like ResNet-101. Our results provide strong empirical evidence that using all the available data for training can hurt performance on large scale vision tasks.

This paper introduces an innovative Bayesian machine learning algorithm to draw inference on heterogeneous causal effects in the presence of imperfect compliance (e.g., under an irregular assignment mechanism). We show, through Monte Carlo simulations, that the proposed Bayesian Causal Forest with Instrumental Variable (BCF-IV) algorithm outperforms other machine learning techniques tailored for causal inference (namely, Generalized Random Forest and Causal Trees with Instrumental Variable) in estimating the causal effects. Moreover, we show that it converges to an optimal asymptotic performance in discovering the drivers of heterogeneity in a simulated scenario. BCF-IV sheds a light on the heterogeneity of causal effects in instrumental variable scenarios and, in turn, provides the policy-makers with a relevant tool for targeted policies. Its empirical application evaluates the effects of additional funding on students' performances. The results indicate that BCF-IV could be used to enhance the effectiveness of school funding on students' performance by 3.2 to 3.5 times.

Graph neural networks (GNNs) have achieved lots of success on graph-structured data. In the light of this, there has been increasing interest in studying their representation power. One line of work focuses on the universal approximation of permutation-invariant functions by certain classes of GNNs, and another demonstrates the limitation of GNNs via graph isomorphism tests. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the representation power of GNNs with the language of sigma-algebra, which incorporates both viewpoints. Using this framework, we compare the expressive power of different classes of GNNs as well as other methods on graphs. In particular, we prove that order-2 Graph G-invariant networks fail to distinguish non-isomorphic regular graphs with the same degree. We then extend them to a new architecture, Ring-GNNs, which succeeds on distinguishing these graphs and provides improvements on real-world social network datasets.