No Arabic abstract
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph structure or adding hard constraints to feature-space algorithms. Following a different path, we define a metric regression scheme where we train metric-constrained linear combinations of dissimilarity matrices. The idea is that the input matrices can be pre-computed dissimilarity measures obtained from any kind of available data (e.g. node attributes or edge structure). As the model inputs are distance measures, we do not need to assume the existence of any underlying feature space. Main challenge is that metric constraints (especially positive-definiteness and sub-additivity), are not automatically respected if, for example, the coefficients of the linear combination are allowed to be negative. Both positive and sub-additive constraints are linear inequalities, but the computational complexity of imposing them scales as O(D3), where D is the size of the input matrices (i.e. the size of the data set). This becomes quickly prohibitive, even when D is relatively small. We propose a new graph-based technique for optimizing under such constraints and show that, in some cases, our approach may reduce the original computational complexity of the optimization process by one order of magnitude. Contrarily to existing methods, our scheme applies to any (possibly non-convex) metric-constrained objective function.
Regression problems that have closed-form solutions are well understood and can be easily implemented when the dataset is small enough to be all loaded into the RAM. Challenges arise when data is too big to be stored in RAM to compute the closed form solutions. Many techniques were proposed to overcome or alleviate the memory barrier problem but the solutions are often local optimal. In addition, most approaches require accessing the raw data again when updating the models. Parallel computing clusters are also expected if multiple models need to be computed simultaneously. We propose multiple learning approaches that utilize an array of sufficient statistics (SS) to address this big data challenge. This memory oblivious approach breaks the memory barrier when computing regressions with closed-form solutions, including but not limited to linear regression, weighted linear regression, linear regression with Box-Cox transformation (Box-Cox regression) and ridge regression models. The computation and update of the SS array can be handled at per row level or per mini-batch level. And updating a model is as easy as matrix addition and subtraction. Furthermore, multiple SS arrays for different models can be easily computed simultaneously to obtain multiple models at one pass through the dataset. We implemented our approaches on Spark and evaluated over the simulated datasets. Results showed our approaches can achieve closed-form solutions of multiple models at the cost of half training time of the traditional methods for a single model.
Structured pruning is a well-known technique to reduce the storage size and inference cost of neural networks. The usual pruning pipeline consists of ranking the network internal filters and activations with respect to their contributions to the network performance, removing the units with the lowest contribution, and fine-tuning the network to reduce the harm induced by pruning. Recent results showed that random pruning performs on par with other metrics, given enough fine-tuning resources. In this work, we show that this is not true on a low-data regime when fine-tuning is either not possible or not effective. In this case, reducing the harm caused by pruning becomes crucial to retain the performance of the network. First, we analyze the problem of estimating the contribution of hidden units with tools suggested by cooperative game theory and propose Shapley values as a principled ranking metric for this task. We compare with several alternatives proposed in the literature and discuss how Shapley values are theoretically preferable. Finally, we compare all ranking metrics on the challenging scenario of low-data pruning, where we demonstrate how Shapley values outperform other heuristics.
Multiple instance data are sets or multi-sets of unordered elements. Using metrics or distances for sets, we propose an approach to several multiple instance learning tasks, such as clustering (unsupervised learning), classification (supervised learning), and novelty detection (semi-supervised learning). In particular, we introduce the Optimal Sub-Pattern Assignment metric to multiple instance learning so as to provide versatile design choices. Numerical experiments on both simulated and real data are presented to illustrate the versatility of the proposed solution.
Generative modeling of set-structured data, such as point clouds, requires reasoning over local and global structures at various scales. However, adopting multi-scale frameworks for ordinary sequential data to a set-structured data is nontrivial as it should be invariant to the permutation of its elements. In this paper, we propose SetVAE, a hierarchical variational autoencoder for sets. Motivated by recent progress in set encoding, we build SetVAE upon attentive modules that first partition the set and project the partition back to the original cardinality. Exploiting this module, our hierarchical VAE learns latent variables at multiple scales, capturing coarse-to-fine dependency of the set elements while achieving permutation invariance. We evaluate our model on point cloud generation task and achieve competitive performance to the prior arts with substantially smaller model capacity. We qualitatively demonstrate that our model generalizes to unseen set sizes and learns interesting subset relations without supervision. Our implementation is available at https://github.com/jw9730/setvae.
Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for large scale scenarios. We propose a new family of online proximal algorithms for MKL (as well as for group-lasso and variants thereof), which overcomes that drawback. We show regret, convergence, and generalization bounds for the proposed method. Experiments on handwriting recognition and dependency parsing testify for the successfulness of the approach.