Bandit problems are most commonly thought of in terms of sequential decision making or as an elementary version of reinforcement learning. This is certainly true, but they are also intimately connected with optimisation. These notes focus on the convex bandit problem, where the set of actions is a convex subset of euclidean space and the function mapping actions to losses is convex. The learner chooses actions and observes the corresponding loss, possibly with additive noise. The duty of the learner is to minimise the loss. When phrased like this the problem seems more like zeroth-order optimisation and these notes largely take that viewpoint. We do borrow two key notions from the bandit community that give the algorithms and analysis a unique flavour: We focus on the cumulative regret as a performance criterion; and We (mostly) consider the adversarial setting, where the loss function is changing from one query to the next. These differences mean the algorithms and theorems presented here are often not directly comparable to standard settings in the optimisation literature. Generally speaking, the theorems presented here hold with fewer assumptions and consequentially are sometimes weaker.

Early detection of myocardial infarction (MI), a critical condition arising from coronary artery disease (CAD), is vital to prevent further myocardial damage. This study introduces a novel method for early MI detection using a one-class classification (OCC) algorithm in echocardiography. Our study overcomes the challenge of limited echocardiography data availability by adopting a novel approach based on Multi-modal Subspace Support Vector Data Description. The proposed technique involves a specialized MI detection framework employing multi-view echocardiography incorporating a composite kernel in the non-linear projection trick, fusing Gaussian and Laplacian sigmoid functions. Additionally, we enhance the update strategy of the projection matrices by adapting maximization for both or one of the modalities in the optimization process. Our method boosts MI detection capability by efficiently transforming features extracted from echocardiography data into an optimized lower-dimensional subspace. The OCC model trained specifically on target class instances from the comprehensive HMC-QU dataset that includes multiple echocardiography views indicates a marked improvement in MI detection accuracy. Our findings reveal that our proposed multi-view approach achieves a geometric mean of 71.24\%, signifying a substantial advancement in echocardiography-based MI diagnosis and offering more precise and efficient diagnostic tools.

In the reconstruction of fa\c{c}ade elements, the identification of specific object types remains challenging and is often circumvented by rectangularity assumptions or the use of bounding boxes. We propose a new approach for the reconstruction of 3D fa\c{c}ade details. We combine MLS point clouds and a pre-defined 3D model library using a BoW concept, which we augment by incorporating semi-global features. We conduct experiments on the models superimposed with random noise and on the TUM-FA\c{C}ADE dataset. Our method demonstrates promising results, improving the conventional BoW approach. It holds the potential to be utilized for more realistic facade reconstruction without rectangularity assumptions, which can be used in applications such as testing automated driving functions or estimating fa\c{c}ade solar potential.

The clinical trial is a pivotal and costly process, often spanning multiple years and requiring substantial financial resources. Therefore, the development of clinical trial outcome prediction models aims to exclude drugs likely to fail and holds the potential for significant cost savings. Recent data-driven attempts leverage deep learning methods to integrate multimodal data for predicting clinical trial outcomes. However, these approaches rely on manually designed modal-specific encoders, which limits both the extensibility to adapt new modalities and the ability to discern similar information patterns across different modalities. To address these issues, we propose a multimodal mixture-of-experts (LIFTED) approach for clinical trial outcome prediction. Specifically, LIFTED unifies different modality data by transforming them into natural language descriptions. Then, LIFTED constructs unified noise-resilient encoders to extract information from modal-specific language descriptions. Subsequently, a sparse Mixture-of-Experts framework is employed to further refine the representations, enabling LIFTED to identify similar information patterns across different modalities and extract more consistent representations from those patterns using the same expert model. Finally, a mixture-of-experts module is further employed to dynamically integrate different modality representations for prediction, which gives LIFTED the ability to automatically weigh different modalities and pay more attention to critical information. The experiments demonstrate that LIFTED significantly enhances performance in predicting clinical trial outcomes across all three phases compared to the best baseline, showcasing the effectiveness of our proposed key components.

Private data analysis faces a significant challenge known as the curse of dimensionality, leading to increased costs. However, many datasets possess an inherent low-dimensional structure. For instance, during optimization via gradient descent, the gradients frequently reside near a low-dimensional subspace. If the low-dimensional structure could be privately identified using a small amount of points, we could avoid paying (in terms of privacy and accuracy) for the high ambient dimension. On the negative side, Dwork, Talwar, Thakurta, and Zhang (STOC 2014) proved that privately estimating subspaces, in general, requires an amount of points that depends on the dimension. But Singhal and Steinke (NeurIPS 2021) bypassed this limitation by considering points that are i.i.d. samples from a Gaussian distribution whose covariance matrix has a certain eigenvalue gap. Yet, it was still left unclear whether we could provide similar upper bounds without distributional assumptions and whether we could prove lower bounds that depend on similar eigenvalue gaps. In this work, we make progress in both directions. We formulate the problem of private subspace estimation under two different types of singular value gaps of the input data and prove new upper and lower bounds for both types. In particular, our results determine what type of gap is sufficient and necessary for estimating a subspace with an amount of points that is independent of the dimension.

Time series analysis is relevant in various disciplines such as physics, biology, chemistry, and Time series analysis plays a pivotal role in extracting valuable finance. In this paper, we present a novel neural insights from sequential data, uncovering patterns, network architecture that integrates elements trends, and underlying structures that drive temporal dynamics from ResNet structures, while introducing the innovative (Zhang, 2003; Tang et al., 1991). The ubiquity incorporation of the Taylor series framework. of time series data across diverse domains, including finance, This approach demonstrates notable enhancements healthcare, and environmental science, underscores in test accuracy across many of the the critical need for accurate and efficient analytical methods baseline datasets investigated.

The Stochastic Gradient Descent (SGD) is extensively used in Deep Learning (see [2]). A direct and simple proof of a convergence result of the SGD is given in [3]. Here we will go further and investigate the convergence rate of the SGD, giving some elementary proofs, for two choices of the "learning rate", both in the class of'inverse time decay' schedules.

Irregular sampling of time series in electronic health records (EHRs) is one of the main challenges for developing machine learning models. Additionally, the pattern of missing data in certain clinical variables is not at random but depends on the decisions of clinicians and the state of the patient. Point process is a mathematical framework for analyzing event sequence data that is consistent with irregular sampling patterns. Our model, TEE4EHR, is a transformer event encoder (TEE) with point process loss that encodes the pattern of laboratory tests in EHRs. The utility of our TEE has been investigated in a variety of benchmark event sequence datasets. Additionally, we conduct experiments on two real-world EHR databases to provide a more comprehensive evaluation of our model. Firstly, in a self-supervised learning approach, the TEE is jointly learned with an existing attention-based deep neural network which gives superior performance in negative log-likelihood and future event prediction. Besides, we propose an algorithm for aggregating attention weights that can reveal the interaction between the events. Secondly, we transfer and freeze the learned TEE to the downstream task for the outcome prediction, where it outperforms state-of-the-art models for handling irregularly sampled time series. Furthermore, our results demonstrate that our approach can improve representation learning in EHRs and can be useful for clinical prediction tasks.

In recent years Deep Neural Network-based systems are not only increasing in popularity but also receive growing user trust. However, due to the closed-world assumption of such systems, they cannot recognize samples from unknown classes and often induce an incorrect label with high confidence. Presented work looks at the evaluation of methods for Open Set Recognition, focusing on the impact of class imbalance, especially in the dichotomy between known and unknown samples. As an outcome of problem analysis, we present a set of guidelines for evaluation of methods in this field.

Background. A main theoretical puzzle is why over-parameterized Neural Networks (NNs) generalize well when trained to zero loss (i.e., so they interpolate the data). Usually, the NN is trained with Stochastic Gradient Descent (SGD) or one of its variants. However, recent empirical work examined the generalization of a random NN that interpolates the data: the NN was sampled from a seemingly uniform prior over the parameters, conditioned on that the NN perfectly classifying the training set. Interestingly, such a NN sample typically generalized as well as SGD-trained NNs. Contributions. We prove that such a random NN interpolator typically generalizes well if there exists an underlying narrow ``teacher NN" that agrees with the labels. Specifically, we show that such a `flat' prior over the NN parametrization induces a rich prior over the NN functions, due to the redundancy in the NN structure. In particular, this creates a bias towards simpler functions, which require less relevant parameters to represent -- enabling learning with a sample complexity approximately proportional to the complexity of the teacher (roughly, the number of non-redundant parameters), rather than the student's.