Many weakly supervised classification methods employ a noise transition matrix to capture the class-conditional label corruption. To estimate the transition matrix from noisy data, existing methods often need to estimate the noisy class-posterior, which could be unreliable due to the overconfidence of neural networks. In this work, we propose a theoretically grounded method that can estimate the noise transition matrix and learn a classifier simultaneously, without relying on the error-prone noisy class-posterior estimation. Concretely, inspired by the characteristics of the stochastic label corruption process, we propose total variation regularization, which encourages the predicted probabilities to be more distinguishable from each other. Under mild assumptions, the proposed method yields a consistent estimator of the transition matrix. We show the effectiveness of the proposed method through experiments on benchmark and real-world datasets.

We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online active learning algorithm that runs in polynomial time, and under the conditions that the marginal distribution is isotropic log-concave and $\nu = \Omega(\epsilon)$, where $\epsilon \in (0, 1)$ is the target error rate, our algorithm PAC learns the underlying halfspace with near-optimal label complexity of $\tilde{O}\big(d \cdot \polylog(\frac{1}{\epsilon})\big)$ and sample complexity of $\tilde{O}\big(\frac{d}{\epsilon} \big)$. Prior to this work, existing online algorithms designed for tolerating the adversarial noise are subject to either label complexity polynomial in $\frac{1}{\epsilon}$, or suboptimal noise tolerance, or restrictive marginal distributions. With the additional prior knowledge that the underlying halfspace is $s$-sparse, we obtain attribute-efficient label complexity of $\tilde{O}\big( s \cdot \polylog(d, \frac{1}{\epsilon}) \big)$ and sample complexity of $\tilde{O}\big(\frac{s}{\epsilon} \cdot \polylog(d) \big)$. As an immediate corollary, we show that under the agnostic model where no assumption is made on the noise rate $\nu$, our active learner achieves an error rate of $O(OPT) + \epsilon$ with the same running time and label and sample complexity, where $OPT$ is the best possible error rate achievable by any homogeneous halfspace.

The healthcare industry generates troves of unlabelled physiological data. This data can be exploited via contrastive learning, a self-supervised pre-training method that encourages representations of instances to be similar to one another. We propose a family of contrastive learning methods, CLOCS, that encourages representations across space, time, \textit{and} patients to be similar to one another. We show that CLOCS consistently outperforms the state-of-the-art methods, BYOL and SimCLR, when performing a linear evaluation of, and fine-tuning on, downstream tasks. We also show that CLOCS achieves strong generalization performance with only 25\% of labelled training data. Furthermore, our training procedure naturally generates patient-specific representations that can be used to quantify patient-similarity.

Machine learning approached through supervised learning requires expensive annotation of data. This motivates weakly supervised learning, where data are annotated with incomplete yet discriminative information. In this paper, we focus on partial labelling, an instance of weak supervision where, from a given input, we are given a set of potential targets. We review a disambiguation principle to recover full supervision from weak supervision, and propose an empirical disambiguation algorithm. We prove exponential convergence rates of our algorithm under classical learnability assumptions, and we illustrate the usefulness of our method on practical examples.

We analyze the problem of active covering, where the learner is given an unlabeled dataset and can sequentially label query examples. The objective is to label query all of the positive examples in the fewest number of total label queries. We show under standard non-parametric assumptions that a classical support estimator can be repurposed as an offline algorithm attaining an excess query cost of $\widetilde{\Theta}(n^{D/(D+1)})$ compared to the optimal learner, where $n$ is the number of datapoints and $D$ is the dimension. We then provide a simple active learning method that attains an improved excess query cost of $\widetilde{O}(n^{(D-1)/D})$. Furthermore, the proposed algorithms only require access to the positive labeled examples, which in certain settings provides additional computational and privacy benefits. Finally, we show that the active learning method consistently outperforms offline methods as well as a variety of baselines on a wide range of benchmark image-based datasets.

Ordinary supervised learning is useful when we have paired training data of input $X$ and output $Y$. However, such paired data can be difficult to collect in practice. In this paper, we consider the task of predicting $Y$ from $X$ when we have no paired data of them, but we have two separate, independent datasets of $X$ and $Y$ each observed with some mediating variable $U$, that is, we have two datasets $S_X = \{(X_i, U_i)\}$ and $S_Y = \{(U'_j, Y'_j)\}$. A naive approach is to predict $U$ from $X$ using $S_X$ and then $Y$ from $U$ using $S_Y$, but we show that this is not statistically consistent. Moreover, predicting $U$ can be more difficult than predicting $Y$ in practice, e.g., when $U$ has higher dimensionality. To circumvent the difficulty, we propose a new method that avoids predicting $U$ but directly learns $Y = f(X)$ by training $f(X)$ with $S_{X}$ to predict $h(U)$ which is trained with $S_{Y}$ to approximate $Y$. We prove statistical consistency and error bounds of our method and experimentally confirm its practical usefulness.

We consider a linear autoencoder in which the latent variables are quantized, or corrupted by noise, and the constraint is Schur-concave in the set of latent variances. Although finding the optimal encoder/decoder pair for this setup is a nonconvex optimization problem, we show that decomposing the source into its principal components is optimal. If the constraint is strictly Schur-concave and the empirical covariance matrix has only simple eigenvalues, then any optimal encoder/decoder must decompose the source in this way. As one application, we consider a strictly Schur-concave constraint that estimates the number of bits needed to represent the latent variables under fixed-rate encoding, a setup that we call \emph{Principal Bit Analysis (PBA)}. This yields a practical, general-purpose, fixed-rate compressor that outperforms existing algorithms. As a second application, we show that a prototypical autoencoder-based variable-rate compressor is guaranteed to decompose the source into its principal components.