## Posts

### Explainable 2-means Clustering: Five Lines Proof

In a previous post, we discussed tree-based clustering and how to develop explainable clustering algorithms with provable guarantees. Now we will show*why*only one feature is enough to define a good 2-means clustering. And we will do it using only 5 inequalities (!)### Explainable k-means Clustering

Popular algorithms for learning decision trees can be arbitrarily bad for clustering. We present a new algorithm for explainable clustering that has provable guarantees --- the Iterative Mistake Minimization (IMM) algorithm. This algorithm exhibits good results in practice. It's running time is comparable to KMeans implemented in sklearn. So our method gives you explanations basically for free. Our code is available on github.### Towards Physics-informed Deep Learning for Turbulent Flow Prediction

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call turbulent-Flow Net (TF-Net), is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model, TF-Net, with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.### How to Detect Data-Copying in Generative Models

What does it mean for a generative model to overfit? We formalize the notion of 'data-copying', when a generative model produces only slight variations of the training set and fails to express the diversity of the true distribution. To catch this form of overfitting, we propose a three-sample hypothesis test that is entirely model agnostic. Our experiments indicate that several standard tests condone data-copying, and contemporary generative models like VAEs and GANs can commit data-copying.### The Power of Comparison: Reliable Active Learning

In the world of big data, large but costly to label datasets dominate many fields. Active learning, a semi-supervised alternative to the standard PAC-learning model, was introduced to explore whether adaptive labeling could learn concepts with exponentially fewer labeled samples. Unfortunately, it is well known that in standard models, active learning provides little improvement over passive learning for the foundational classes such as linear separators. We discuss how empowering the learner to compare points resolves not only this issue, but also allows us to build efficient algorithms which make no errors at all!### Adversarial Robustness for Non-Parametric Classifiers

Adversarial robustness has received much attention recently. Prior defenses and attacks for non-parametric classifiers have been developed on a classifier-specific basis. In this post, we take a holistic view and present a defense and an attack algorithm that are applicable across many non-parametric classifiers. Our defense algorithm, adversarial pruning, works by preprocessing the dataset so the data is better separated. It can be interpreted as a finite sample approximation to the optimally robust classifier. The attack algorithm, region-based attack, works by decomposing the feature space into convex regions. We show that our defense and attack have good empirical performance over a range of datasets.### Adversarial Robustness Through Local Lipschitzness

Robustness often leads to lower test accuracy, which is undesirable. We prove that (i) if the dataset is separated, then there always exists a robust and accurate classifier, and (ii) this classifier can be obtained by rounding a locally Lipschitz function. Empirically, we verify that popular datasets (MNIST, CIFAR-10, and ImageNet) are separated, and we show that neural networks with a small local Lipschitz constant indeed have high test accuracy and robustness.

subscribe via RSS