However, in a surprise to approximately no one who works professionally with data, we do not live in an ideal world. A variety of pressures compel many practitioners to perform tens, hundreds, or even thousands of significance tests on the same data set. Some reasons for doing this are better than others but, independent of even the very best motivations: this practice basically breaks everyday statistics. The assurance of a getting small p-value–that chance alone would spur null differences to appear this distinct only 5%, 1%, 0.1% of the time–is moot when you're playing the odds hundreds, thousands, or tens of thousands of times. A really really big number divided by a big number [or, equivalently here, multiplied by a small proportion] is still a really really big number.

We study the spectrum of inner-product kernel matrices, i.e., $n \times n$ matrices with entries $h (\langle \textbf{x}_i ,\textbf{x}_j \rangle/d)$ where the $( \textbf{x}_i)_{i \leq n}$ are i.i.d.~random covariates in $\mathbb{R}^d$. In the linear high-dimensional regime $n \asymp d$, it was shown that these matrices are well approximated by their linearization, which simplifies into the sum of a rescaled Wishart matrix and identity matrix. In this paper, we generalize this decomposition to the polynomial high-dimensional regime $n \asymp d^\ell,\ell \in \mathbb{N}$, for data uniformly distributed on the sphere and hypercube. In this regime, the kernel matrix is well approximated by its degree-$\ell$ polynomial approximation and can be decomposed into a low-rank spike matrix, identity and a `Gegenbauer matrix' with entries $Q_\ell (\langle \textbf{x}_i , \textbf{x}_j \rangle)$, where $Q_\ell$ is the degree-$\ell$ Gegenbauer polynomial. We show that the spectrum of the Gegenbauer matrix converges in distribution to a Marchenko-Pastur law. This problem is motivated by the study of the prediction error of kernel ridge regression (KRR) in the polynomial regime $n \asymp d^\kappa, \kappa >0$. Previous work showed that for $\kappa \not\in \mathbb{N}$, KRR fits exactly a degree-$\lfloor \kappa \rfloor$ polynomial approximation to the target function. In this paper, we use our characterization of the kernel matrix to complete this picture and compute the precise asymptotics of the test error in the limit $n/d^\kappa \to \psi$ with $\kappa \in \mathbb{N}$. In this case, the test error can present a double descent behavior, depending on the effective regularization and signal-to-noise ratio at level $\kappa$. Because this double descent can occur each time $\kappa$ crosses an integer, this explains the multiple descent phenomenon in the KRR risk curve observed in several previous works.

Due to the COVID 19 pandemic, smartphone-based proximity tracing systems became of utmost interest. Many of these systems use BLE signals to estimate the distance between two persons. The quality of this method depends on many factors and, therefore, does not always deliver accurate results. In this paper, we present a multi-channel approach to improve proximity classification, and a novel, publicly available data set that contains matched IEEE 802.11 (2.4 GHz and 5 GHz) and BLE signal strength data, measured in four different environments. We have developed and evaluated a combined classification model based on BLE and IEEE 802.11 signals. Our approach significantly improves the distance classification and consequently also the contact tracing accuracy. We are able to achieve good results with our approach in everyday public transport scenarios. However, in our implementation based on IEEE 802.11 probe requests, we also encountered privacy problems and limitations due to the consistency and interval at which such probes are sent. We discuss these limitations and sketch how our approach could be improved to make it suitable for real-world deployment.

Data science is not easy, we all know that. Even programming requires a lot of your cycles to get fully onboarded. Don't get me wrong, I love being a developer to some extent, but is hard. You can read and watch a ton of videos about how easy is to get into programming, but as with everything in life, if you are not passionate, you may find some roadblocks along the way. I get it, you may be thinking, "Nice way to start a post!, I'm out dude", but, let me tell you that even though becoming a data scientist is a challenge, as we are becoming more data-centric, data-aware, and data-dependent, you need to sort these issues out to become a specialist, that's part of the journey.

We propose the AdaPtive Noise Augmentation (PANDA) procedure to regularize the estimation and inference of generalized linear models (GLMs). PANDA iteratively optimizes the objective function given noise augmented data until convergence to obtain the regularized model estimates. The augmented noises are designed to achieve various regularization effects, including $l_0$, bridge (lasso and ridge included), elastic net, adaptive lasso, and SCAD, as well as group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function and establish the almost sure convergence of the noise-augmented loss function and its minimizer to the expected penalized loss function and its minimizer, respectively. We derive the asymptotic distributions for the regularized parameters, based on which, inferences can be obtained simultaneously with variable selection. PANDA exhibits ensemble learning behaviors that help further decrease the generalization error. Computationally, PANDA is easy to code, leveraging existing software for implementing GLMs, without resorting to complicated optimization techniques. We demonstrate the superior or similar performance of PANDA against the existing approaches of the same type of regularizers in simulated and real-life data. We show that the inferences through PANDA achieve nominal or near-nominal coverage and are far more efficient compared to a popular existing post-selection procedure.

Caltech/MIT's LIGO, the largest gravitational-wave observatory in the world, collects data on minute space-time ripples from cataclysmic astronomical events like colliding black holes or supernovae. Classifying LIDO's data as either an event of interest or an unknown "glitch" with high accuracy poses a challenge, due to the volume of highly complex data collected by the observatory. A recent dissertation by Columbia University's Robert Colgan [1] proposes a neural network to accurately separate non-astrophysical glitches, achieving significantly higher classification accuracy than previous methods. Gravitational waves, first proposed by Einstein in his general theory of relativity, are caused by massive objects -- like black holes--curving spacetime. The waves ripple through the universe at the speed of light, distorting space and time as they compress and stretch distances.

Nowadays, there are outstanding strides towards a future with autonomous vehicles on our roads. While the perception of autonomous vehicles performs well under closed-set conditions, they still struggle to handle the unexpected. This survey provides an extensive overview of anomaly detection techniques based on camera, lidar, radar, multimodal and abstract object level data. We provide a systematization including detection approach, corner case level, ability for an online application, and further attributes. We outline the state-of-the-art and point out current research gaps.

Machine learning and Artificial Intelligence models have gained promising results in recent years. The major factor behind their success is the availability and development of vast datasets. However, regardless of how many terabytes of data you have or how skilled you are at data science, machine learning models will be useless and even dangerous if you can't make sense of data records. A slice is a collection of data samples with a common feature. For example, in a picture dataset, photographs of antique vehicles make up a slice.

Measures to predict 30-day readmission are considered an important quality factor for hospitals as accurate predictions can reduce the overall cost of care by identifying high risk patients before they are discharged. While recent deep learning-based studies have shown promising empirical results on readmission prediction, several limitations exist that may hinder widespread clinical utility, such as (a) only patients with certain conditions are considered, (b) existing approaches do not leverage data temporality, (c) individual admissions are assumed independent of each other, which is unrealistic, (d) prior studies are usually limited to single source of data and single center data. To address these limitations, we propose a multimodal, modality-agnostic spatiotemporal graph neural network (MM-STGNN) for prediction of 30-day all-cause hospital readmission that fuses multimodal in-patient longitudinal data. By training and evaluating our methods using longitudinal chest radiographs and electronic health records from two independent centers, we demonstrate that MM-STGNN achieves AUROC of 0.79 on both primary and external datasets. Furthermore, MM-STGNN significantly outperforms the current clinical reference standard, LACE+ score (AUROC=0.61), on the primary dataset. For subset populations of patients with heart and vascular disease, our model also outperforms baselines on predicting 30-day readmission (e.g., 3.7 point improvement in AUROC in patients with heart disease). Lastly, qualitative model interpretability analysis indicates that while patients' primary diagnoses were not explicitly used to train the model, node features crucial for model prediction directly reflect patients' primary diagnoses. Importantly, our MM-STGNN is agnostic to node feature modalities and could be utilized to integrate multimodal data for triaging patients in various downstream resource allocation tasks.

Counterfactual explanations have been widely studied in explainability, with a range of application dependent methods emerging in fairness, recourse and model understanding. However, the major shortcoming associated with these methods is their inability to provide explanations beyond the local or instance-level. While some works touch upon the notion of a global explanation, typically suggesting to aggregate masses of local explanations in the hope of ascertaining global properties, few provide frameworks that are either reliable or computationally tractable. Meanwhile, practitioners are requesting more efficient and interactive explainability tools. We take this opportunity to investigate existing global methods, with a focus on implementing and improving Actionable Recourse Summaries (AReS), the only known global counterfactual explanation framework for recourse.