Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen widespread use in machine learning. In this work, we aim to bridge this gap by exploring the use of tilting in risk minimization. We study a simple extension to ERM -- tilted empirical risk minimization (TERM) -- which uses exponential tilting to flexibly tune the impact of individual losses. The resulting framework has several useful properties: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to a superquantile method. Our work makes rigorous connections between TERM and related objectives, such as Value-at-Risk, Conditional Value-at-Risk, and distributionally robust optimization (DRO). We develop batch and stochastic first-order optimization methods for solving TERM, provide convergence guarantees for the solvers, and show that the framework can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications in machine learning, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. Despite the straightforward modification TERM makes to traditional ERM objectives, we find that the framework can consistently outperform ERM and deliver competitive performance with state-of-the-art, problem-specific approaches.

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the rank minimization of a nonlinear feature map applied to the original matrix, which is then further approximated by a constrained non-convex optimization problem involving the Grassmann manifold. We propose two sets of algorithms, one arising from Riemannian optimization and the other as an alternating minimization scheme, both of which include first- and second-order variants. Both sets of algorithms have theoretical guarantees. In particular, for the alternating minimization, we establish global convergence and worst-case complexity bounds. Additionally, using the Kurdyka-Lojasiewicz property, we show that the alternating minimization converges to a unique limit point. We provide extensive numerical results for the recovery of union of subspaces and clustering under entry sampling and dense Gaussian sampling. Our methods are competitive with existing approaches and, in particular, high accuracy is achieved in the recovery using Riemannian second-order methods.

This paper introduces V-SysId, a novel method that enables simultaneous keypoint discovery, 3D system identification, and extrinsic camera calibration from an unlabeled video taken from a static camera, using only the family of equations of motion of the object of interest as weak supervision. V-SysId takes keypoint trajectory proposals and alternates between maximum likelihood parameter estimation and extrinsic camera calibration, before applying a suitable selection criterion to identify the track of interest. This is then used to train a keypoint tracking model using supervised learning. Results on a range of settings (robotics, physics, physiology) highlight the utility of this approach.

"Know thy data" is one of the fundamental principles of sound data science. Another name for this is data profiling. I simply refer to it as "having your first date with your data." We expand on data profiling here by elucidating the following four steps toward knowing your data: (1) data preview and selection; (2) data cleansing and preparation; (3) feature selection and engineering; and (4) data typing for normalization and transformation. Knowledge of your data begins with a thorough preview of the good, bad and ugly parts of your data collection, and it ultimately leads to a decision about which portions of the data set you will select for your data science analysis.

Ensemble Learning is taking the predictions of multiple models and assume the output to be having the most votes. When you train multiple Decision Trees each on some random sampling of the dataset and for predictions you take predictions of all the trees, the output class would be the class which gets the most votes. This approach is called Random Forest. Voting classifier is when you train the data on multiple classifier such as Logistic Regression, SVM, RF and other classifiers and the majority vote is the predicted output class ie hard classifier. Voting can also be taken as soft by taking argmax of the outputs.

In statistics, a test of significance is a method of reaching a conclusion to either reject or accept certain claims based on the data. In the case of regression analysis, it is used to determine whether an independent variable is significant in explaining the variance of the dependent variable. Since here we have only one predictor a T-test should be enough. However, in reality, our model is going to include a number of independent variables. This is where F-statistic comes into play.

Modern neural networks can assign high confidence to inputs drawn from outside the training distribution, posing threats to models in real-world deployments. While much research attention has been placed on designing new out-of-distribution (OOD) detection methods, the precise definition of OOD is often left in vagueness and falls short of the desired notion of OOD in reality. In this paper, we present a new formalization and model the data shifts by taking into account both the invariant and environmental (spurious) features. Under such formalization, we systematically investigate how spurious correlation in the training set impacts OOD detection. Our results suggest that the detection performance is severely worsened when the correlation between spurious features and labels is increased in the training set. We further show insights on detection methods that are more effective in reducing the impact of spurious correlation and provide theoretical analysis on why reliance on environmental features leads to high OOD detection error. Our work aims to facilitate a better understanding of OOD samples and their formalization, as well as the exploration of methods that enhance OOD detection.

The fingerprint classification is an important and effective method to quicken the process and improve the accuracy in the fingerprint matching process. Conventional supervised methods need a large amount of pre-labeled data and thus consume immense human resources. In this paper, we propose a new and efficient unsupervised deep learning method that can extract fingerprint features and classify fingerprint patterns automatically. In this approach, a new model named constraint convolutional auto-encoder (CCAE) is used to extract fingerprint features and a hybrid clustering strategy is applied to obtain the final clusters. A set of experiments in the NIST-DB4 dataset shows that the proposed unsupervised method exhibits the efficient performance on fingerprint classification. For example, the CCAE achieves an accuracy of 97.3% on only 1000 unlabeled fingerprints in the NIST-DB4.

Real world learning scenarios involve a nonstationary distribution of classes with sequential dependencies among the samples, in contrast to the standard machine learning formulation of drawing samples independently from a fixed, typically uniform distribution. Furthermore, real world interactions demand learning on-the-fly from few or no class labels. In this work, we propose an unsupervised model that simultaneously performs online visual representation learning and few-shot learning of new categories without relying on any class labels. Our model is a prototype-based memory network with a control component that determines when to form a new class prototype. We formulate it as an online Gaussian mixture model, where components are created online with only a single new example, and assignments do not have to be balanced, which permits an approximation to natural imbalanced distributions from uncurated raw data. Learning includes a contrastive loss that encourages different views of the same image to be assigned to the same prototype. The result is a mechanism that forms categorical representations of objects in nonstationary environments. Experiments show that our method can learn from an online stream of visual input data and is significantly better at category recognition compared to state-of-the-art self-supervised learning methods.

In practice, machine learning (ML) workflows require various different steps, from data preprocessing, missing value imputation, model selection, to model tuning as well as model evaluation. Many of these steps rely on human ML experts. AutoML - the field of automating these ML pipelines - tries to help practitioners to apply ML off-the-shelf without any expert knowledge. Most modern AutoML systems like auto-sklearn, H20-AutoML or TPOT aim for high predictive performance, thereby generating ensembles that consist almost exclusively of black-box models. This, in turn, makes the interpretation for the layperson more intricate and adds another layer of opacity for users. We propose an AutoML system that constructs an interpretable additive model that can be fitted using a highly scalable componentwise boosting algorithm. Our system provides tools for easy model interpretation such as visualizing partial effects and pairwise interactions, allows for a straightforward calculation of feature importance, and gives insights into the required model complexity to fit the given task. We introduce the general framework and outline its implementation autocompboost. To demonstrate the frameworks efficacy, we compare autocompboost to other existing systems based on the OpenML AutoML-Benchmark. Despite its restriction to an interpretable model space, our system is competitive in terms of predictive performance on most data sets while being more user-friendly and transparent.