Deep supervised learning has achieved great success in various applications, including computer vision (Krizhevsky et al., 2012), natural language processing (Devlin et al., 2018), and scientific computing (Han et al., 2018). However, its dependence on manually assigned labels, which is usually difficult and costly, has motivated research into alternative approaches to exploit unlabeled data. Self-supervised learning is a promising approach that leverages the unlabeled data itself as supervision and learns representations that are beneficial to potential downstream tasks. At a high level, there are two common approaches for feature extraction in self-supervised learning: generative and contrastive (Liu et al., 2021). Both approaches aim to learn latent representations of the original data, while the difference is that the generative approach focused on minimizing the reconstruction error from latent representations, and the contrastive approach targets to decrease the similarity between the representations of contrastive pairs. Recent works have shown the benefits of contrastive learning in practice (Chen et al., 2020a,b,c; He et al., 2020).

In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.

We present $\Delta$-UQ -- a novel, general-purpose uncertainty estimator using the concept of anchoring in predictive models. Anchoring works by first transforming the input into a tuple consisting of an anchor point drawn from a prior distribution, and a combination of the input sample with the anchor using a pretext encoding scheme. This encoding is such that the original input can be perfectly recovered from the tuple -- regardless of the choice of the anchor. Therefore, any predictive model should be able to predict the target response from the tuple alone (since it implicitly represents the input). Moreover, by varying the anchors for a fixed sample, we can estimate uncertainty in the prediction even using only a single predictive model. We find this uncertainty is deeply connected to improper sampling of the input data, and inherent noise, enabling us to estimate the total uncertainty in any system. With extensive empirical studies on a variety of use-cases, we demonstrate that $\Delta$-UQ outperforms several competitive baselines. Specifically, we study model fitting, sequential model optimization, model based inversion in the regression setting and out of distribution detection, & calibration under distribution shifts for classification.

We introduce Noisy Feature Mixup (NFM), an inexpensive yet effective method for data augmentation that combines the best of interpolation based training and noise injection schemes. Rather than training with convex combinations of pairs of examples and their labels, we use noise-perturbed convex combinations of pairs of data points in both input and feature space. This method includes mixup and manifold mixup as special cases, but it has additional advantages, including better smoothing of decision boundaries and enabling improved model robustness. We provide theory to understand this as well as the implicit regularization effects of NFM. Our theory is supported by empirical results, demonstrating the advantage of NFM, as compared to mixup and manifold mixup. We show that residual networks and vision transformers trained with NFM have favorable trade-offs between predictive accuracy on clean data and robustness with respect to various types of data perturbation across a range of computer vision benchmark datasets.

We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3.5 times better compression performance than the algorithms based on a neural-network autoencoder and principal component analysis. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.

Background: Survival analysis concerns the study of timeline data where the event of interest may remain unobserved (i.e., censored). Studies commonly record more than one type of event, but conventional survival techniques focus on a single event type. We set out to integrate both multiple independently censored time-to-event variables as well as missing observations. Methods: An energy-based approach is taken with a bi-partite structure between latent and visible states, commonly known as harmoniums (or restricted Boltzmann machines). Results: The present harmonium is shown, both theoretically and experimentally, to capture non-linear patterns between distinct time recordings. We illustrate on real world data that, for a single time-to-event variable, our model is on par with established methods. In addition, we demonstrate that discriminative predictions improve by leveraging an extra time-to-event variable. Conclusions: Multiple time-to-event variables can be successfully captured within the harmonium paradigm.

We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p \times p$ covariance matrix $\Sigma$ exhibits a spiked eigenvalues structure and the vector $\zeta$, given by the difference between the whitened mean vectors, is sparse with sparsity at most $s$. We propose an adaptive classifier (adaptive with respect to the sparsity $s$) that first performs dimension reduction on the feature vectors prior to classification in the dimensionally reduced space, i.e., the classifier whitened the data, then screen the features by keeping only those corresponding to the $s$ largest coordinates of $\zeta$ and finally apply Fisher linear discriminant on the selected features. Leveraging recent results on entrywise matrix perturbation bounds for covariance matrices, we show that the resulting classifier is Bayes optimal whenever $n \rightarrow \infty$ and $s \sqrt{n^{-1} \ln p} \rightarrow 0$. Experimental results on real and synthetic data sets indicate that the proposed classifier is competitive with existing state-of-the-art methods while also selecting a smaller number of features.

In this article, we investigate the spectral behavior of random features kernel matrices of the type ${\bf K} = \mathbb{E}_{{\bf w}} \left[\sigma\left({\bf w}^{\sf T}{\bf x}_i\right)\sigma\left({\bf w}^{\sf T}{\bf x}_j\right)\right]_{i,j=1}^n$, with nonlinear function $\sigma(\cdot)$, data ${\bf x}_1, \ldots, {\bf x}_n \in \mathbb{R}^p$, and random projection vector ${\bf w} \in \mathbb{R}^p$ having i.i.d. entries. In a high-dimensional setting where the number of data $n$ and their dimension $p$ are both large and comparable, we show, under a Gaussian mixture model for the data, that the eigenspectrum of ${\bf K}$ is independent of the distribution of the i.i.d.(zero-mean and unit-variance) entries of ${\bf w}$, and only depends on $\sigma(\cdot)$ via its (generalized) Gaussian moments $\mathbb{E}_{z\sim \mathcal N(0,1)}[\sigma'(z)]$ and $\mathbb{E}_{z\sim \mathcal N(0,1)}[\sigma''(z)]$. As a result, for any kernel matrix ${\bf K}$ of the form above, we propose a novel random features technique, called Ternary Random Feature (TRF), that (i) asymptotically yields the same limiting kernel as the original ${\bf K}$ in a spectral sense and (ii) can be computed and stored much more efficiently, by wisely tuning (in a data-dependent manner) the function $\sigma$ and the random vector ${\bf w}$, both taking values in $\{-1,0,1\}$. The computation of the proposed random features requires no multiplication, and a factor of $b$ times less bits for storage compared to classical random features such as random Fourier features, with $b$ the number of bits to store full precision values. Besides, it appears in our experiments on real data that the substantial gains in computation and storage are accompanied with somewhat improved performances compared to state-of-the-art random features compression/quantization methods.

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.

Design of experiments (DOE) is playing an essential role in learning and improving a variety of objects and processes. The article discusses the application of unsupervised machine learning to support the pragmatic designs of complex experiments. Complex experiments are characterized by having a large number of factors, mixed-level designs, and may be subject to constraints that eliminate some unfeasible trials for various reasons. Having such attributes, it is very challenging to design pragmatic experiments that are economically, operationally, and timely sound. It means a significant decrease in the number of required trials from a full factorial design, while still attempting to achieve the defined objectives. A beta variational autoencoder (beta-VAE) has been applied to represent trials of the initial full factorial design after filtering out unfeasible trials on the low dimensional latent space. Regarding visualization and interpretability, the paper is limited to 2D representations. Beta-VAE supports (1) orthogonality of the latent space dimensions, (2) isotropic multivariate standard normal distribution of the representation on the latent space, (3) disentanglement of the latent space representation by levels of factors, (4) propagation of the applied constraints of the initial design into the latent space, and (5) generation of trials by decoding latent space points. Having an initial design representation on the latent space with such properties, it allows for the generation of pragmatic design of experiments (G-DOE) by specifying the number of trials and their pattern on the latent space, such as square or polar grids. Clustering and aggregated gradient metrics have been shown to guide grid specification.