Survival Analysis provides critical insights for partially incomplete time-to-event data in various domains. It is also an important example of probabilistic machine learning. The probabilistic nature of the predictions can be exploited by using (proper) scoring rules in the model fitting process instead of likelihood-based optimization. Our proposal does so in a generic manner and can be used for a variety of model classes. We establish different parametric and non-parametric sub-frameworks that allow different degrees of flexibility. Incorporated into neural networks, it leads to a computationally efficient and scalable optimization routine, yielding state-of-the-art predictive performance. Finally, we show that using our framework, we can recover various parametric models and demonstrate that optimization works equally well when compared to likelihood-based methods.

A fundamental exercise in machine learning is the approximation of a function of several to many variables given values of the function, often contaminated with noise, at observed joint values of the input variables. The result can then be used to estimate unknown function values given corresponding inputs. The goal is to accurately estimate the underlying (non noisy) outcome values since the noise is by definition unpredictable. To the extent that this is successful the estimated function may, in addition, be used to try to understand underlying phenomena giving rise to the data. Even when prediction accuracy is the dominate concern, being able to comprehend the way in which the input variables are jointly combining to produce predictions may lead to important sanity checks on the validity of the function estimate. Besides accuracy, the success of this latter exercise requires that the structure of the function estimate be represented in a comprehensible form.

Optimizing an unknown function under safety constraints is a central task in robotics, biomedical engineering, and many other disciplines, and increasingly safe Bayesian Optimization (BO) is used for this. Due to the safety critical nature of these applications, it is of utmost importance that theoretical safety guarantees for these algorithms translate into the real world. In this work, we investigate three safety-related issues of the popular class of SafeOpt-type algorithms. First, these algorithms critically rely on frequentist uncertainty bounds for Gaussian Process (GP) regression, but concrete implementations typically utilize heuristics that invalidate all safety guarantees. We provide a detailed analysis of this problem and introduce Real-\b{eta}-SafeOpt, a variant of the SafeOpt algorithm that leverages recent GP bounds and thus retains all theoretical guarantees. Second, we identify assuming an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function, a key technical assumption in SafeOpt-like algorithms, as a central obstacle to real-world usage. To overcome this challenge, we introduce the Lipschitz-only Safe Bayesian Optimization (LoSBO) algorithm, which guarantees safety without an assumption on the RKHS bound, and empirically show that this algorithm is not only safe, but also exhibits superior performance compared to the state-of-the-art on several function classes. Third, SafeOpt and derived algorithms rely on a discrete search space, making them difficult to apply to higher-dimensional problems. To widen the applicability of these algorithms, we introduce Lipschitz-only GP-UCB (LoS-GP-UCB), a variant of LoSBO applicable to moderately high-dimensional problems, while retaining safety.

Rankings are a type of preference elicitation that arise in experiments where assessors arrange items, for example, in decreasing order of utility. Orderings of n items labelled {1,...,n} denoted are permutations that reflect strict preferences. For a number of reasons, strict preferences can be unrealistic assumptions for real data. For example, when items share common traits it may be reasonable to attribute them equal ranks. Also, there can be different importance attributions to decisions that form the ranking. In a situation with, for example, a large number of items, an assessor may wish to rank at top a certain number items; to rank other items at the bottom and to express indifference to all others. In addition, when aggregating opinions, a judging body might be decisive about some parts of the rank but ambiguous for others. In this paper we extend the well-known Mallows (Mallows, 1957) model (MM) to accommodate item indifference, a phenomenon that can be in place for a variety of reasons, such as those above mentioned.The underlying grouping of similar items motivates the proposed Clustered Mallows Model (CMM). The CMM can be interpreted as a Mallows distribution for tied ranks where ties are learned from the data. The CMM provides the flexibility to combine strict and indifferent relations, achieving a simpler and robust representation of rank collections in the form of ordered clusters. Bayesian inference for the CMM is in the class of doubly-intractable problems since the model's normalisation constant is not available in closed form. We overcome this challenge by sampling from the posterior with a version of the exchange algorithm \citep{murray2006}. Real data analysis of food preferences and results of Formula 1 races are presented, illustrating the CMM in practical situations.

Gaussian-Bernoulli restricted Boltzmann machines (GBRBMs) are often used for semi-supervised anomaly detection, where they are trained using only normal data points. In GBRBM-based anomaly detection, normal and anomalous data are classified based on a score that is identical to an energy function of the marginal GBRBM. However, the classification threshold is difficult to set to an appropriate value, as this score cannot be interpreted. In this study, we propose a measure that improves score's interpretability based on its cumulative distribution, and establish a guideline for setting the threshold using the interpretable measure. The results of numerical experiments show that the guideline is reasonable when setting the threshold solely using normal data points. Moreover, because identifying the measure involves computationally infeasible evaluation of the minimum score value, we also propose an evaluation method for the minimum score based on simulated annealing, which is widely used for optimization problems. The proposed evaluation method was also validated using numerical experiments.

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular notions of statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fr\'echet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.

Deep representations have shown promising performance when transferred to downstream tasks in a black-box manner. Yet, their inherent lack of interpretability remains a significant challenge, as these features are often opaque to human understanding. In this paper, we propose Non-negative Contrastive Learning (NCL), a renaissance of Non-negative Matrix Factorization (NMF) aimed at deriving interpretable features. The power of NCL lies in its enforcement of non-negativity constraints on features, reminiscent of NMF's capability to extract features that align closely with sample clusters. NCL not only aligns mathematically well with an NMF objective but also preserves NMF's interpretability attributes, resulting in a more sparse and disentangled representation compared to standard contrastive learning (CL). Theoretically, we establish guarantees on the identifiability and downstream generalization of NCL. Empirically, we show that these advantages enable NCL to outperform CL significantly on feature disentanglement, feature selection, as well as downstream classification tasks. At last, we show that NCL can be easily extended to other learning scenarios and benefit supervised learning as well. Code is available at https://github.com/PKU-ML/non_neg. The first two demonstrate top-activated samples along each feature dimension, where those of CL (a) often have distinct semantics along each dimension (column) (e.g., dears and airplanes), while those of NCL (b) have much better semantic consistency, indicating better feature disentanglement. Comparing (c) and (d), it is easy to see that NCL features enjoy much better sparsity than CL features with only a few activated dimensions (< 10%) per sample. It is widely believed that the success of deep learning lies in its ability to learn meaningful representations (Bengio et al., 2013). In recent years, contrastive learning (CL) has further initiated a huge interest in self-supervised learning (SSL) of representations and attained promising performance in various downstream tasks (Chen et al., 2020; Wang et al., 2021; Guo et al., 2023; Luo et al., 2023).

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of $\textit{spectral algorithms}$ specified by profile $h(\lambda)$, and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile $h(\lambda)$ for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Social animals have been found to use some means of communication to coordinate in various contexts: foraging for food, avoiding predators, mating, etc. (Hauser, 1996). Among animals, however, humans seem to be unique in having developed a communication system, natural language, that transcends these basic needs and can represent an infinite variety of new situations (Hauser et al., 2002) to the extent that language itself becomes the basis for a new form of evolution: cultural evolution. Understanding the emergence of this unique human ability has always been a vexing scientific problem due to the lack of access to the communication systems of intermediate steps of hominid evolution (Harnad et al., 1976; Bickerton, 2007). In the absence of data, a tempting idea has been to reproduce experimentally the process of language emergence in either humans or computational models (Steels, 1997; Myers-Scotton, 2002; Kirby, 2002). Experimental paradigms with humans (Kirby et al., 2008; Raviv et al., 2019; Motamedi et al., 2019) have produced significant insights into language evolution. Still, their scope is limited due to the inability to replicate key aspects of language evolution, such as communication within and across large populations and the study of long evolutionary timescales. Computer modeling can help overcome these limitations and has played a prominent role in studying language evolution for a long time (Lieberman and Crelin, 1971).

In this work we address flexibility in deep learning by means of transductive reasoning. For adaptation to new tasks or new data, existing methods typically involve tuning of learnable parameters or even complete re-training from scratch, rendering such approaches unflexible in practice. We argue that the notion of separating computation from memory by the means of transduction can act as a stepping stone for solving these issues. We therefore propose PARMESAN (parameter-free memory search and transduction), a scalable transduction method which leverages a memory module for solving dense prediction tasks. At inference, hidden representations in memory are being searched to find corresponding examples. In contrast to other methods, PARMESAN learns without the requirement for any continuous training or fine-tuning of learnable parameters simply by modifying the memory content. Our method is compatible with commonly used neural architectures and canonically transfers to 1D, 2D, and 3D grid-based data. We demonstrate the capabilities of our approach at complex tasks such as continual and few-shot learning. PARMESAN learns up to 370 times faster than common baselines while being on par in terms of predictive performance, knowledge retention, and data-efficiency.