Machine Learning has attracted considerable attention throughout the past decade due to its potential to solve far-reaching tasks, such as image classification, object recognition, anomaly detection, and data forecasting. A standard approach to tackle such applications is based on supervised learning, which is assisted by large sets of labeled data and is conducted by the so-called classifiers, such as Logistic Regression, Decision Trees, Random Forests, and Support Vector Machines, among others. An alternative to traditional classifiers is the parameterless Optimum-Path Forest (OPF), which uses a graph-based methodology and a distance measure to create arcs between nodes and hence sets of trees, responsible for conquering the nodes, defining their labels, and shaping the forests. Nevertheless, its performance is strongly associated with an appropriate distance measure, which may vary according to the dataset's nature. Therefore, this work proposes a comparative study over a wide range of distance measures applied to the supervised Optimum-Path Forest classification. The experimental results are conducted using well-known literature datasets and compared across benchmarking classifiers, illustrating OPF's ability to adapt to distinct domains.

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods for deep neural networks, building on both the variational Bayesian and Markov chain Monte Carlo (MCMC) frameworks. A fundamental issue with MCMC methods is that the improvements they enable are obtained at the expense of increased computation time and model storage costs. In this paper, we investigate the potential of sparse network structures to flexibly trade-off model storage costs and inference run time against predictive performance and uncertainty quantification ability. We use stochastic gradient MCMC methods as the core Bayesian inference method and consider a variety of approaches for selecting sparse network structures. Surprisingly, our results show that certain classes of randomly selected substructures can perform as well as substructures derived from state-of-the-art iterative pruning methods while drastically reducing model training times.

Optimization of real-world black-box functions defined over purely categorical variables is an active area of research. In particular, optimization and design of biological sequences with specific functional or structural properties have a profound impact in medicine, materials science, and biotechnology. Standalone search algorithms, such as simulated annealing (SA) and Monte Carlo tree search (MCTS), are typically used for such optimization problems. In order to improve the performance and sample efficiency of such algorithms, we propose to use existing methods in conjunction with a surrogate model for the black-box evaluations over purely categorical variables. To this end, we present two different representations, a group-theoretic Fourier expansion and an abridged one-hot encoded Boolean Fourier expansion. To learn such representations, we consider two different settings to update our surrogate model. First, we utilize an adversarial online regression setting where Fourier characters of each representation are considered as experts and their respective coefficients are updated via an exponential weight update rule each time the black box is evaluated. Second, we consider a Bayesian setting where queries are selected via Thompson sampling and the posterior is updated via a sparse Bayesian regression model (over our proposed representation) with a regularized horseshoe prior. Numerical experiments over synthetic benchmarks as well as real-world RNA sequence optimization and design problems demonstrate the representational power of the proposed methods, which achieve competitive or superior performance compared to state-of-the-art counterparts, while improving the computation cost and/or sample efficiency, substantially.

We study the problem of unsupervised skill discovery, whose goal is to learn a set of diverse and useful skills with no external reward. There have been a number of skill discovery methods based on maximizing the mutual information (MI) between skills and states. However, we point out that their MI objectives usually prefer static skills to dynamic ones, which may hinder the application for downstream tasks. To address this issue, we propose Lipschitz-constrained Skill Discovery (LSD), which encourages the agent to discover more diverse, dynamic, and far-reaching skills. Another benefit of LSD is that its learned representation function can be utilized for solving goal-following downstream tasks even in a zero-shot manner - i.e., without further training or complex planning. Through experiments on various MuJoCo robotic locomotion and manipulation environments, we demonstrate that LSD outperforms previous approaches in terms of skill diversity, state space coverage, and performance on seven downstream tasks including the challenging task of following multiple goals on Humanoid. Our code and videos are available at https://shpark.me/projects/lsd/.

The statistical machine learning community has demonstrated considerable resourcefulness over the years in developing highly expressive tools for estimation, prediction, and inference. The bedrock assumptions underlying these developments are that the data comes from a fixed population and displays little heterogeneity. But reality is significantly more complex: statistical models now routinely fail when released into real-world systems and scientific applications, where such assumptions rarely hold. Consequently, we pursue a different path in this paper vis-a-vis the well-worn trail of developing new methodology for estimation and prediction. In this paper, we develop tools and theory for detecting and identifying regions of the covariate space (subpopulations) where model performance has begun to degrade, and study intervening to fix these failures through refitting. We present empirical results with three real-world data sets -- including a time series involving forecasting the incidence of COVID-19 -- showing that our methodology generates interpretable results, is useful for tracking model performance, and can boost model performance through refitting. We complement these empirical results with theory proving that our methodology is minimax optimal for recovering anomalous subpopulations as well as refitting to improve accuracy in a structured normal means setting.

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral or Frobenius norms. In this paper, we provide entrywise $\ell_{2,\infty}$ bounds for Sparse PCA under a general high-dimensional subgaussian design. In particular, our results hold for any algorithm that selects the correct support with high probability, those that are sparsistent. Our bound improves upon known results by providing a finer characterization of the estimation error, and our proof uses techniques recently developed for entrywise subspace perturbation theory.

We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\reals^n$, $k<

In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We propose a novel weak supervision algorithm that processes noisy labels, i.e., weak signals, while also considering features of the training data to produce accurate labels for training. Our method searches over classifiers of the data representation to find plausible labelings. We call this paradigm data consistent weak supervision. A key facet of our framework is that we are able to estimate labels for data examples low or no coverage from the weak supervision. In addition, we make no assumptions about the joint distribution of the weak signals and true labels of the data. Instead, we use weak signals and the data features to solve a constrained optimization that enforces data consistency among the labels we generate. Empirical evaluation of our method on different datasets shows that it significantly outperforms state-of-the-art weak supervision methods on both text and image classification tasks.

We present a meta-method for initializing (seeding) the $k$-means clustering algorithm called PNN-smoothing. It consists in splitting a given dataset into $J$ random subsets, clustering each of them individually, and merging the resulting clusterings with the pairwise-nearest-neighbor (PNN) method. It is a meta-method in the sense that when clustering the individual subsets any seeding algorithm can be used. If the computational complexity of that seeding algorithm is linear in the size of the data $N$ and the number of clusters $k$, PNN-smoothing is also almost linear with an appropriate choice of $J$, and in fact only at most a few percent slower in most cases in practice. We show empirically, using several existing seeding methods and testing on several synthetic and real datasets, that this procedure results in systematically better costs. It can even be applied recursively, and easily parallelized. Our implementation is publicly available at https://github.com/carlobaldassi/KMeansPNNSmoothing.jl

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of its adjacency or Laplacian matrix, and has found applications throughout the sciences. Many such networks are multipartite, meaning their nodes can be divided into partitions and nodes of the same partition are never connected. When the network is multipartite, this paper demonstrates that the node representations obtained via spectral embedding live near partition-specific low-dimensional subspaces of a higher-dimensional ambient space. For this reason we propose a follow-on step after spectral embedding, to recover node representations in their intrinsic rather than ambient dimension, proving uniform consistency under a low-rank, inhomogeneous random graph model. Our method naturally generalizes bipartite spectral embedding, in which node representations are obtained by singular value decomposition of the biadjacency or bi-Laplacian matrix.