Neural networks are usually trained with different variants of gradient descent based optimization algorithms such as stochastic gradient descent or the Adam optimizer. Recent theoretical work states that the critical points (where the gradient of the loss is zero) of two-layer ReLU networks with the square loss are not all local minima. However, in this work we will explore an algorithm for training two-layer neural networks with ReLU-like activation and the square loss that alternatively finds the critical points of the loss function analytically for one layer while keeping the other layer and the neuron activation pattern fixed. Experiments indicate that this simple algorithm can find deeper optima than Stochastic Gradient Descent or the Adam optimizer, obtaining significantly smaller training loss values on four out of the five real datasets evaluated. Moreover, the method is faster than the gradient descent methods and has virtually no tuning parameters.

Parametric verification of linear temporal properties for stochastic models can be expressed as computing the satisfaction probability of a certain property as a function of the parameters of the model. Smoothed model checking (smMC) aims at inferring the satisfaction function over the entire parameter space from a limited set of observations obtained via simulation. As observations are costly and noisy, smMC is framed as a Bayesian inference problem so that the estimates have an additional quantification of the uncertainty. In smMC the authors use Gaussian Processes (GP), inferred by means of the Expectation Propagation algorithm. This approach provides accurate reconstructions with statistically sound quantification of the uncertainty. However, it inherits the well-known scalability issues of GP. In this paper, we exploit recent advances in probabilistic machine learning to push this limitation forward, making Bayesian inference of smMC scalable to larger datasets and enabling its application to models with high dimensional parameter spaces. We propose Stochastic Variational Smoothed Model Checking (SV-smMC), a solution that exploits stochastic variational inference (SVI) to approximate the posterior distribution of the smMC problem. The strength and flexibility of SVI make SV-smMC applicable to two alternative probabilistic models: Gaussian Processes (GP) and Bayesian Neural Networks (BNN). The core ingredient of SVI is a stochastic gradient-based optimization that makes inference easily parallelizable and that enables GPU acceleration. In this paper, we compare the performances of smMC against those of SV-smMC by looking at the scalability, the computational efficiency and the accuracy of the reconstructed satisfaction function.

Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.

Machine learning models often fail to generalize well under distributional shifts. Understanding and overcoming these failures have led to a research field of Out-of-Distribution (OOD) generalization. Despite being extensively studied for static computer vision tasks, OOD generalization has been underexplored for time series tasks. To shine light on this gap, we present WOODS: eight challenging open-source time series benchmarks covering a diverse range of data modalities, such as videos, brain recordings, and sensor signals. We revise the existing OOD generalization algorithms for time series tasks and evaluate them using our systematic framework. Our experiments show a large room for improvement for empirical risk minimization and OOD generalization algorithms on our datasets, thus underscoring the new challenges posed by time series tasks. Code and documentation are available at https://woods-benchmarks.github.io .

Feature selection has been widely used to alleviate compute requirements during training, elucidate model interpretability, and improve model generalizability. We propose SLM -- Sparse Learnable Masks -- a canonical approach for end-to-end feature selection that scales well with respect to both the feature dimension and the number of samples. At the heart of SLM lies a simple but effective learnable sparse mask, which learns which features to select, and gives rise to a novel objective that provably maximizes the mutual information (MI) between the selected features and the labels, which can be derived from a quadratic relaxation of mutual information from first principles. In addition, we derive a scaling mechanism that allows SLM to precisely control the number of features selected, through a novel use of sparsemax. This allows for more effective learning as demonstrated in ablation studies. Empirically, SLM achieves state-of-the-art results against a variety of competitive baselines on eight benchmark datasets, often by a significant margin, especially on those with real-world challenges such as class imbalance.

Although real-time facial emotion recognition is a hot topic research domain in the field of human-computer interaction, state-of the-art available datasets still suffer from various problems, such as some unrelated photos such as document photos, unbalanced numbers of photos in each class, and misleading images that can negatively affect correct classification. The 3RL dataset was created, which contains approximately 24K images and will be publicly available, to overcome previously available dataset problems. The 3RL dataset is labelled with five basic emotions: happiness, fear, sadness, disgust, and anger. Moreover, we compared the 3RL dataset with other famous state-of-the-art datasets (FER dataset, CK+ dataset), and we applied the most commonly used algorithms in previous works, SVM and CNN. The results show a noticeable improvement in generalization on the 3RL dataset. Experiments have shown an accuracy of up to 91.4% on 3RL dataset using CNN where results on FER2013, CK+ are, respectively (approximately from 60% to 85%).

We settle the complexity of dynamic least-squares regression (LSR), where rows and labels $(\mathbf{A}^{(t)}, \mathbf{b}^{(t)})$ can be adaptively inserted and/or deleted, and the goal is to efficiently maintain an $\epsilon$-approximate solution to $\min_{\mathbf{x}^{(t)}} \| \mathbf{A}^{(t)} \mathbf{x}^{(t)} - \mathbf{b}^{(t)} \|_2$ for all $t\in [T]$. We prove sharp separations ($d^{2-o(1)}$ vs. $\sim d$) between the amortized update time of: (i) Fully vs. Partially dynamic $0.01$-LSR; (ii) High vs. low-accuracy LSR in the partially-dynamic (insertion-only) setting. Our lower bounds follow from a gap-amplification reduction -- reminiscent of iterative refinement -- rom the exact version of the Online Matrix Vector Conjecture (OMv) [HKNS15], to constant approximate OMv over the reals, where the $i$-th online product $\mathbf{H}\mathbf{v}^{(i)}$ only needs to be computed to $0.1$-relative error. All previous fine-grained reductions from OMv to its approximate versions only show hardness for inverse polynomial approximation $\epsilon = n^{-\omega(1)}$ (additive or multiplicative) . This result is of independent interest in fine-grained complexity and for the investigation of the OMv Conjecture, which is still widely open.

A long-standing goal of machine-learning-based protein engineering is to accelerate the discovery of novel mutations that improve the function of a known protein. We introduce a sampling framework for evolving proteins in silico that supports mixing and matching a variety of unsupervised models, such as protein language models, and supervised models that predict protein function from sequence. By composing these models, we aim to improve our ability to evaluate unseen mutations and constrain search to regions of sequence space likely to contain functional proteins. Our framework achieves this without any model fine-tuning or re-training by constructing a product of experts distribution directly in discrete protein space. Instead of resorting to brute force search or random sampling, which is typical of classic directed evolution, we introduce a fast MCMC sampler that uses gradients to propose promising mutations. We conduct in silico directed evolution experiments on wide fitness landscapes and across a range of different pre-trained unsupervised models, including a 650M parameter protein language model. Our results demonstrate an ability to efficiently discover variants with high evolutionary likelihood as well as estimated activity multiple mutations away from a wild type protein, suggesting our sampler provides a practical and effective new paradigm for machine-learning-based protein engineering.

News sources undergo the process of selecting newsworthy information when covering a certain topic. The process inevitably exhibits selection biases, i.e. news sources' typical patterns of choosing what information to include in news coverage, due to their agenda differences. To understand the magnitude and implications of selection biases, one must first discover (1) on what topics do sources typically have diverging definitions of "newsworthy" information, and (2) do the content selection patterns correlate with certain attributes of the news sources, e.g. ideological leaning, etc. The goal of the paper is to investigate and discuss the challenges of building scalable NLP systems for discovering patterns of media selection biases directly from news content in massive-scale news corpora, without relying on labeled data. To facilitate research in this domain, we propose and study a conceptual framework, where we compare how sources typically mention certain controversial entities, and use such as indicators for the sources' content selection preferences. We empirically show the capabilities of the framework through a case study on NELA-2020, a corpus of 1.8M news articles in English from 519 news sources worldwide. We demonstrate an unsupervised representation learning method to capture the selection preferences for how sources typically mention controversial entities. Our experiments show that that distributional divergence of such representations, when studied collectively across entities and news sources, serve as good indicators for an individual source's ideological leaning. We hope our findings will provide insights for future research on media selection biases.

This paper considers the well-studied algorithmic regime of designing a $(1+\epsilon)$-approximation algorithm for a $k$-clustering problem that runs in time $f(k,\epsilon)poly(n)$ (sometimes called an efficient parameterized approximation scheme or EPAS for short). Notable results of this kind include EPASes in the high-dimensional Euclidean setting for $k$-center [Bad\u{o}iu, Har-Peled, Indyk; STOC'02] as well as $k$-median, and $k$-means [Kumar, Sabharwal, Sen; J. ACM 2010]. However, existing EPASes handle only basic objectives (such as $k$-center, $k$-median, and $k$-means) and are tailored to the specific objective and metric space. Our main contribution is a clean and simple EPAS that settles more than ten clustering problems (across multiple well-studied objectives as well as metric spaces) and unifies well-known EPASes. Our algorithm gives EPASes for a large variety of clustering objectives (for example, $k$-means, $k$-center, $k$-median, priority $k$-center, $\ell$-centrum, ordered $k$-median, socially fair $k$-median aka robust $k$-median, or more generally monotone norm $k$-clustering) and metric spaces (for example, continuous high-dimensional Euclidean spaces, metrics of bounded doubling dimension, bounded treewidth metrics, and planar metrics). Key to our approach is a new concept that we call bounded $\epsilon$-scatter dimension--an intrinsic complexity measure of a metric space that is a relaxation of the standard notion of bounded doubling dimension. Our main technical result shows that two conditions are essentially sufficient for our algorithm to yield an EPAS on the input metric $M$ for any clustering objective: (i) The objective is described by a monotone (not necessarily symmetric!) norm, and (ii) the $\epsilon$-scatter dimension of $M$ is upper bounded by a function of $\epsilon$.