Job interviews make everyone nervous. But this is what they are designed to do. It is the most common medium to assess a candidate's presence of mind and his/her ability to remain calm and composed in a tense situation. In order to ace the interview, you need to have in-depth knowledge of the role you are interviewing for and what is expected. Presence of mind and strong subject knowledge assumes added significance when you are preparing for a Data Scientist's interview as it is definitely going to test your capabilities.

Unsupervised mixture learning (UML) aims at identifying linearly or nonlinearly mixed latent components in a blind manner. UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g., independent component analysis or nonnegative matrix factorization. In this work, the post-nonlinear (PNL) mixture model -- where unknown element-wise nonlinear functions are imposed onto a linear mixture -- is revisited. The PNL model is widely employed in different fields ranging from brain signal classification, speech separation, remote sensing, to causal discovery. To identify and remove the unknown nonlinear functions, existing works often assume different properties on the latent components (e.g., statistical independence or probability-simplex structures). This work shows that under a carefully designed UML criterion, the existence of a nontrivial null space associated with the underlying mixing system suffices to guarantee identification/removal of the unknown nonlinearity. Compared to prior works, our finding largely relaxes the conditions of attaining PNL identifiability, and thus may benefit applications where no strong structural information on the latent components is known. A finite-sample analysis is offered to characterize the performance of the proposed approach under realistic settings. To implement the proposed learning criterion, a block coordinate descent algorithm is proposed. A series of numerical experiments corroborate our theoretical claims.

A new implementation of an adiabatically-trained ensemble model is derived that shows significant improvements over classical methods. In particular, empirical results of this new algorithm show that it offers not just higher performance, but also more stability with less classifiers, an attribute that is critically important in areas like explainability and speed-of-inference. In all, the empirical analysis displays that the algorithm can provide an increase in performance on unseen data by strengthening stability of the statistical model through further minimizing and balancing variance and bias, while decreasing the time to convergence over its predecessors.

For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every number between one and the number of data, the result is a function, the cluster structure function. It maps the number of parts of a partition to values related to the deficiencies of being good models by the parts. Such a function starts with a value at least zero for no partition of the data set and descents to zero for the partition of the data set into singleton parts. The optimal clustering is the one chosen to minimize the cluster structure function. The theory behind the method is expressed in algorithmic information theory (Kolmogorov complexity). In practice the Kolmogorov complexities involved are approximated by a concrete compressor. We give examples using real data sets: the MNIST handwritten digits and the segmentation of real cells as used in stem cell research.

Hand, the bearer of human productivity and intelligence, is receiving much attention due to the recent fever of digital twins. Among different hand morphable models, MANO has been widely used in vision and graphics community. However, MANO disregards textures and accessories, which largely limits its power to synthesize photorealistic hand data. In this paper, we extend MANO with Diverse Accessories and Rich Textures, namely DART. DART is composed of 50 daily 3D accessories which varies in appearance and shape, and 325 hand-crafted 2D texture maps covers different kinds of blemishes or make-ups. Unity GUI is also provided to generate synthetic hand data with user-defined settings, e.g., pose, camera, background, lighting, textures, and accessories. Finally, we release DARTset, which contains large-scale (800K), high-fidelity synthetic hand images, paired with perfect-aligned 3D labels. Experiments demonstrate its superiority in diversity. As a complement to existing hand datasets, DARTset boosts the generalization in both hand pose estimation and mesh recovery tasks. Raw ingredients (textures, accessories), Unity GUI, source code and DARTset are publicly available at dart2022.github.io

We provide the first complete continuous time framework for denoising diffusion models of discrete data. This is achieved by formulating the forward noising process and corresponding reverse time generative process as Continuous Time Markov Chains (CTMCs). The model can be efficiently trained using a continuous time version of the ELBO. We simulate the high dimensional CTMC using techniques developed in chemical physics and exploit our continuous time framework to derive high performance samplers that we show can outperform discrete time methods for discrete data. The continuous time treatment also enables us to derive a novel theoretical result bounding the error between the generated sample distribution and the true data distribution.

Sliced mutual information (SMI) is defined as an average of mutual information (MI) terms between one-dimensional random projections of the random variables. It serves as a surrogate measure of dependence to classic MI that preserves many of its properties but is more scalable to high dimensions. However, a quantitative characterization of how SMI itself and estimation rates thereof depend on the ambient dimension, which is crucial to the understanding of scalability, remain obscure. This work provides a multifaceted account of the dependence of SMI on dimension, under a broader framework termed $k$-SMI, which considers projections to $k$-dimensional subspaces. Using a new result on the continuity of differential entropy in the 2-Wasserstein metric, we derive sharp bounds on the error of Monte Carlo (MC)-based estimates of $k$-SMI, with explicit dependence on $k$ and the ambient dimension, revealing their interplay with the number of samples. We then combine the MC integrator with the neural estimation framework to provide an end-to-end $k$-SMI estimator, for which optimal convergence rates are established. We also explore asymptotics of the population $k$-SMI as dimension grows, providing Gaussian approximation results with a residual that decays under appropriate moment bounds. All our results trivially apply to SMI by setting $k=1$. Our theory is validated with numerical experiments and is applied to sliced InfoGAN, which altogether provide a comprehensive quantitative account of the scalability question of $k$-SMI, including SMI as a special case when $k=1$.

Algorithmic fairness has received increased attention in socially sensitive domains. While rich literature on mean fairness has been established, research on quantile fairness remains sparse but vital. To fulfill great needs and advocate the significance of quantile fairness, we propose a novel framework to learn a real-valued quantile function under the fairness requirement of Demographic Parity with respect to sensitive attributes, such as race or gender, and thereby derive a reliable fair prediction interval. Using optimal transport and functional synchronization techniques, we establish theoretical guarantees of distribution-free coverage and exact fairness for the induced prediction interval constructed by fair quantiles. A hands-on pipeline is provided to incorporate flexible quantile regressions with an efficient fairness adjustment post-processing algorithm. We demonstrate the superior empirical performance of this approach on several benchmark datasets. Our results show the model's ability to uncover the mechanism underlying the fairness-accuracy trade-off in a wide range of societal and medical applications.

Driving trajectory representation learning is of great significance for various location-based services, such as driving pattern mining and route recommendation. However, previous representation generation approaches tend to rarely address three challenges: 1) how to represent the intricate semantic intentions of mobility inexpensively; 2) complex and weak spatial-temporal dependencies due to the sparsity and heterogeneity of the trajectory data; 3) route selection preferences and their correlation to driving behavior. In this paper, we propose a novel multimodal fusion model, DouFu, for trajectory representation joint learning, which applies multimodal learning and attention fusion module to capture the internal characteristics of trajectories. We first design movement, route, and global features generated from the trajectory data and urban functional zones and then analyze them respectively with the attention encoder or feed forward network. The attention fusion module incorporates route features with movement features to create a better spatial-temporal embedding. With the global semantic feature, DouFu produces a comprehensive embedding for each trajectory. We evaluate representations generated by our method and other baseline models on classification and clustering tasks. Empirical results show that DouFu outperforms other models in most of the learning algorithms like the linear regression and the support vector machine by more than 10%.

Deploying models on target domain data subject to distribution shift requires adaptation. Test-time training (TTT) emerges as a solution to this adaptation under a realistic scenario where access to full source domain data is not available and instant inference on target domain is required. Despite many efforts into TTT, there is a confusion over the experimental settings, thus leading to unfair comparisons. In this work, we first revisit TTT assumptions and categorize TTT protocols by two key factors. Among the multiple protocols, we adopt a realistic sequential test-time training (sTTT) protocol, under which we further develop a test-time anchored clustering (TTAC) approach to enable stronger test-time feature learning. TTAC discovers clusters in both source and target domain and match the target clusters to the source ones to improve generalization. Pseudo label filtering and iterative updating are developed to improve the effectiveness and efficiency of anchored clustering. We demonstrate that under all TTT protocols TTAC consistently outperforms the state-of-the-art methods on six TTT datasets. We hope this work will provide a fair benchmarking of TTT methods and future research should be compared within respective protocols.