Label tree-based algorithms are widely used to tackle multi-class and multi-label problems with a large number of labels. We focus on a particular subclass of these algorithms that use probabilistic classifiers in the tree nodes. Examples of such algorithms are hierarchical softmax (HSM), designed for multi-class classification, and probabilistic label trees (PLTs) that generalize HSM to multi-label problems. If the tree structure is given, learning of PLT can be solved with provable regret guaranties [Wydmuch et.al. 2018]. However, to find a tree structure that results in a PLT with a low training and prediction computational costs as well as low statistical error seems to be a very challenging problem, not well-understood yet. In this paper, we address the problem of finding a tree structure that has low computational cost. First, we show that finding a tree with optimal training cost is NP-complete, nevertheless there are some tractable special cases with either perfect approximation or exact solution that can be obtained in linear time in terms of the number of labels $m$. For the general case, we obtain $O(\log m)$ approximation in linear time too. Moreover, we prove an upper bound on the expected prediction cost expressed in terms of the expected training cost. We also show that under additional assumptions the prediction cost of a PLT is $O(\log m)$.

Estimating regression coefficients using unordered multisets of covariates and responses has been introduced as the regression without correspondence problem. Previous theoretical analysis of the problem has been done in a setting where the responses are a permutation of the regressed covariates. This paper expands the setting by analyzing the problem where they may be missing correspondences and outliers in addition to a permutation action. We term this problem robust regression without correspondence and provide several algorithms for exact and approximate recovery in a noiseless and noisy one-dimensional setting as well as an approximation algorithm for multiple dimensions. The theoretical guarantees of the algorithms are verified in simulation data. We also demonstrate a neuroscience application by obtaining robust point set matchings of the neurons of the model organism Caenorhabditis elegans.

The learning of deep models, in which a numerous of parameters are superimposed, is known to be a fairly sensitive process and should be carefully done through a combination of several techniques that can help to stabilize it. We introduce an additional challenge that has never been explicitly studied: the heterogeneity of sparsity at the instance level due to missing values or the innate nature of the input distribution. We confirm experimentally on the widely used benchmark datasets that this variable sparsity problem makes the output statistics of neurons unstable and makes the learning process more difficult by saturating non-linearities. We also provide the analysis of this phenomenon, and based on our analysis, we present a simple technique to prevent this issue, referred to as Sparsity Normalization (SN). Finally, we show that the performance can be significantly improved with SN on certain popular benchmark datasets, or that similar performance can be achieved with lower capacity. Especially focusing on the collaborative filtering problem where the variable sparsity issue has been completely ignored, we achieve new state-of-the-art results on Movielens 100k and 1M datasets, by simply applying Sparsity Normalization (SN).

The problem of learning logical rules from examples arises in diverse fields, including program synthesis, logic programming, and machine learning. Existing approaches either involve solving computationally difficult combinatorial problems, or performing parameter estimation in complex statistical models. In this paper, we present Difflog, a technique to extend the logic programming language Datalog to the continuous setting. By attaching real-valued weights to individual rules of a Datalog program, we naturally associate numerical values with individual conclusions of the program. Analogous to the strategy of numerical relaxation in optimization problems, we can now first determine the rule weights which cause the best agreement between the training labels and the induced values of output tuples, and subsequently recover the classical discrete-valued target program from the continuous optimum. We evaluate Difflog on a suite of 34 benchmark problems from recent literature in knowledge discovery, formal verification, and database query-by-example, and demonstrate significant improvements in learning complex programs with recursive rules, invented predicates, and relations of arbitrary arity.

A new machine learning model allows for physicians to determine whether atypical ductal hyperplasia (ADH) could upgrade to cancer, according to new research published in JCO Clinical Cancer Informatics. The model can identify 98 percent of all malignant cases prior to surgery, while sparing 16 percent of women from unnecessary surgeries on benign lesions. ADH is a breast lesion that increases the risk of breast cancer by four- to five-fold. Typically, ADH is found with mammography and its presence confirmed using biopsy. Previous research published in Current Problems in Diagnostic Radiology found that 95 percent of breast imagers recommend surgical removal for all ADH cases discovered during biopsy to establish if the lesion is cancerous.

Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. We propose an approach to integrate a differentiable proxy for common graph optimization problems into training of machine learning models for tasks such as link prediction. This allows the model to focus specifically on the downstream task that its predictions will be used for. Experimental results show that our end-to-end system obtains better performance on example optimization tasks than can be obtained by combining state of the art link prediction methods with expert-designed graph optimization algorithms.

Most of the work on interpretable machine learning has focused on designing either inherently interpretable models, which typically trade-off accuracy for interpretability, or post-hoc explanation systems, which lack guarantees about their explanation quality. We propose an alternative to these approaches by directly regularizing a black-box model for interpretability at training time. Our approach explicitly connects three key aspects of interpretable machine learning: (i) the model's innate explainability, (ii) the explanation system used at test time, and (iii) the metrics that measure explanation quality. Our regularization results in substantial improvement in terms of the explanation fidelity and stability metrics across a range of datasets and black-box explanation systems while slightly improving accuracy. Further, if the resulting model is still not sufficiently interpretable, the weight of the regularization term can be adjusted to achieve the desired trade-off between accuracy and interpretability. Finally, we justify theoretically that the benefits of explanation-based regularization generalize to unseen points.

Graph neural networks (GNNs) are shown to be successful in modeling applications with graph structures. However, training an accurate GNN model requires a large collection of labeled data and expressive features, which might be inaccessible for some applications. To tackle this problem, we propose a pre-training framework that captures generic graph structural information that is transferable across tasks. Our framework can leverage the following three tasks: 1) denoising link reconstruction, 2) centrality score ranking, and 3) cluster preserving. The pre-training procedure can be conducted purely on the synthetic graphs, and the pre-trained GNN is then adapted for downstream applications. With the proposed pre-training procedure, the generic structural information is learned and preserved, thus the pre-trained GNN requires less amount of labeled data and fewer domain-specific features to achieve high performance on different downstream tasks. Comprehensive experiments demonstrate that our proposed framework can significantly enhance the performance of various tasks at the level of node, link, and graph.

Although optimization is the longstanding algorithmic backbone of machine learning, new models still require the time-consuming implementation of new solvers. As a result, there are thousands of implementations of optimization algorithms for machine learning problems. A natural question is, if it is always necessary to implement a new solver, or if there is one algorithm that is sufficient for most models. Common belief suggests that such a one-algorithm-fits-all approach cannot work, because this algorithm cannot exploit model specific structure and thus cannot be efficient and robust on a wide variety of problems. Here, we challenge this common belief. We have designed and implemented the optimization framework GENO (GENeric Optimization) that combines a modeling language with a generic solver. GENO generates a solver from the declarative specification of an optimization problem class. The framework is flexible enough to encompass most of the classical machine learning problems. We show on a wide variety of classical but also some recently suggested problems that the automatically generated solvers are (1) as efficient as well-engineered specialized solvers, (2) more efficient by a decent margin than recent state-of-the-art solvers, and (3) orders of magnitude more efficient than classical modeling language plus solver approaches.

We present a new generalization error bound, the \emph{PAC-Bayesian transportation bound}, unifying the PAC-Bayesian analysis and the generic chaining method in view of the optimal transportation. The proposed bound is the first PAC-Bayesian framework that characterizes the cost of de-randomization of stochastic predictors facing any Lipschitz loss functions. As an example, we give an upper bound on the de-randomization cost of spectrally normalized neural networks~(NNs) to evaluate how much randomness contributes to the generalization of NNs.