Vector quantization is a fundamental model for image coding, but large codebooks require a long training and encoding time. This can be sped up with tree-structured codes. We propose the use of sparse oblique decision trees, which have hyperplane splits with few nonzero weights in the decision nodes. Such trees can be trained on a dataset of image patches using tree alternating optimization. Experimentally with different datasets, we show these trees consistently achieve a low distortion, close to that of a flat codebook, and a much faster encoding, exceeding other tree-structured vector quantizers.

Building on previous work, we propose a specific form of neurosymbolic model consisting of the composition of convolutional neural network layers with a sparse oblique classification tree (having hyperplane splits using few features). This can be seen as a neural feature extraction that finds a more suitable representation of the input space followed by a form of rule-based reasoning to arrive at a decision that can be explained. We show how to control the sparsity across the different decision nodes of the tree and its effect on the explanations produced. We demonstrate this on image classification tasks and show, among other things, that relatively small subsets of neurons are entirely responsible for the classification into specific classes, and that the neurons’ receptive fields focus on areas of the image that provide best discrimination.

The robustness of human social networks against epidemic propagation relies on the propensity for physical contact adaptation. During the early phase of infection, asymptomatic carriers exhibit the same activity level as susceptible individuals, which presents challenges for incorporating control measures in epidemic projection models. This article focuses on modeling and cost-efficient activity control of susceptible and carrier individuals in the context of the susceptible-carrier-infected-removed (SCIR) epidemic model over a two-layer contact network. In this model, individuals switch from a static contact layer to create new links in a temporal layer based on state-dependent activation rates. We derive conditions for the infection to die out or persist in a homogeneous network. Considering the significant costs associated with reducing the activity of susceptible and carrier individuals, we formulate an optimization problem to minimize the disease decay rate while constrained by a limited budget. We propose the use of successive geometric programming (SGP) approximation for this optimization task. Through simulation experiments on Poisson random graphs, we assess the impact of different parameters on disease prevalence. The results demonstrate that our SGP framework achieves a cost reduction of nearly 33% compared to conventional methods based on degree and closeness centrality.

Univariate decision trees, commonly used since the 1950s, predict by asking questions about a single feature in each decision node. While they are interpretable, they often lack competitive predictive accuracy due to their inability to model feature correlations. Multivariate (oblique) trees use multiple features in each node, capturing high-dimensional correlations better, but sometimes they can be difficult to interpret. We advocate for a model that strikes a useful middle ground: bivariate decision trees, which use two features in each node. This typically produces trees that not only are more accurate than univariate trees, but much smaller, which offsets the small increase in node complexity and keeps them interpretable. They also help data mining by constructing new features that are useful for discrimination, and by providing a form of supervised, hierarchical 2D visualization that reveals patterns such as clusters or linear structure. We give two new algorithms to learn bivariate trees: a fast one based on CART; and a slower one based on alternating optimization with a feature regularization term, which produces the best trees while still scaling to large datasets.

NLP tasks such as language models or document classification involve classification problems with thousands of classes. In these situations, it is difficult to get high predictive accuracy and the resulting model can be huge in number of parameters and inference time. A recent, successful approach is the softmax tree (ST): a decision tree having sparse hyperplane splits at the decision nodes (which make hard, not soft, decisions) and small softmax classifiers at the leaves. Inference here is very fast because only a small subset of class probabilities need to be computed, yet the model is quite accurate. However, a significant drawback is that it assumes a complete tree, whose size grows exponentially with depth. We propose a new algorithm to train a ST of arbitrary structure. The tree structure itself is learned optimally by interleaving steps that grow the structure with steps that optimize the parameters of the current structure. This makes it possible to learn STs that can grow much deeper but in an irregular way, adapting to the data distribution. The resulting STs improve considerably the predictive accuracy while reducing the model size and inference time even further, as demonstrated in datasets with thousands of classes. In addition, they are interpretable to some extent.