Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

As deep neural networks are deployed in safety-critical domains such as autonomous driving and medical diagnosis, stakeholders need explanations that are interpretable but also trustworthy with formal guarantees. Existing XAI methods fall short: heuristic attribution techniques (e.g., LIME, Integrated Gradients) highlight influential features but offer no mathematical guarantees about decision boundaries, while formal methods verify robustness yet remain untargeted, analyzing the nearest boundary regardless of whether it represents a critical risk. In safety-critical systems, not all misclassifications carry equal consequences; confusing a "Stop" sign for a "60 kph" sign is far more dangerous than confusing it with a "No Passing" sign. We introduce ViTaX (Verified and Targeted Explanations), a formal XAI framework that generates targeted semifactual explanations with mathematical guarantees. For a given input (class y) and a user-specified critical alternative (class t), ViTaX: (1) identifies the minimal feature subset most sensitive to the y->t transition, and (2) applies formal reachability analysis to guarantee that perturbing these features by epsilon cannot flip the classification to t. We formalize this through Targeted epsilon-Robustness, certifying whether a feature subset remains robust under perturbation toward a specific target class. ViTaX is the first method to provide formally guaranteed explanations of a model's resilience against user-identified alternatives. Evaluations on MNIST, GTSRB, EMNIST, and TaxiNet demonstrate over 30% fidelity improvement with minimal explanation cardinality.

Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our `plug-and-play' framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.

We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent this structure by a weighted directed graph, where the edge weights are related to the quality of the feedback shared by the connected nodes. Our main contribution is an efficient algorithm that guarantees a regret of $\widetilde{O}(\sqrt{α^* T})$ after $T$ rounds, where $α^*$ is a novel graph property that we call the effective independence number. Our algorithm is completely parameter-free and does not require knowledge (or even estimation) of $α^*$. For the special case of binary edge weights, our setting reduces to the partial-observability models of Mannor and Shamir (2011) and Alon et al. (2013) and our algorithm recovers the near-optimal regret bounds.

In recent years, the widespreadavailability of large-scale, high-dimensionaldatasets has driven significant interest in clustering algorithms that are both computationally efficient and robust to distributional shifts and outliers. The classical clustering method, K-means, can be seen as an application of the Lloyd-Max quantization algorithm, in which the distribution being quantized is the empirical distribution of the points to be clustered. This empirical distribution generally differs from the true underlying distribution, especially when the number of points to be clustered is small. This induces a distributional shift, which can also arise in many real-world settings, such as image segmentation, biological data analysis, and sensor networks, due to noise variations, sensor inaccuracies, or environmental changes. Distributional shifts can severely impact the performance of clustering algorithms, leading to degraded cluster assignments and unreliable downstream analysis. The field of clustering has a rich history. One of the most popular algorithms in this field is theK-means (KM) algorithm, introduced by [1], which computes centroids by iteratively updating the conditional mean of the data in the Voronoi regions induced by the centroids. However, standardK-means is sensitive to initialization and, in general, converges only to a local minimum.

We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test the resulting residuals for marginal independence. This approach yields tests that are sensitive to a broad range of conditional dependencies. Existing methods, however, rely heavily on kernel ridge regression, which is computationally expensive when properly tuned and yields poorly calibrated tests when left untuned, which limits their practical usefulness. We propose the Generalised Kernel Covariance Measure (GKCM), a regression-model-agnostic kernel-based CI test that accommodates a broad class of regression estimators. Building on the Generalised Hilbertian Covariance Measure framework (Lundborg et al., 2022), we characterise conditions under which GKCM satisfies uniform asymptotic level guarantees. In simulations, GKCM paired with tree-based regression models frequently outperforms state-of-the-art CI tests across a diverse range of data-generating processes, achieving better type I error control and competitive or superior power.

Supervised detection of network attacks has always been a critical part of network intrusion detection systems (NIDS). Nowadays, in a pivotal time for artificial intelligence (AI), with even more sophisticated attacks that utilize advanced techniques, such as generative artificial intelligence (GenAI) and reinforcement learning, it has become a vital component if we wish to protect our personal data, which are scattered across the web. In this paper, we address two tasks, in the first unified multi-modal NIDS dataset, which incorporates flow-level data, packet payload information and temporal contextual features, from the reprocessed CIC-IDS-2017, CIC-IoT-2023, UNSW-NB15 and CIC-DDoS-2019, with the same feature space. In the first task we use machine learning (ML) algorithms, with stratified cross validation, in order to prevent network attacks, with stability and reliability. In the second task we use adversarial learning algorithms to generate synthetic data, compare them with the real ones and evaluate their fidelity, utility and privacy using the SDV framework, f-divergences, distinguishability and non-parametric statistical tests. The findings provide stable ML models for intrusion detection and generative models with high fidelity and utility, by combining the Synthetic Data Vault framework, the TRTS and TSTR tests, with non-parametric statistical tests and f-divergence measures.

We revisit the standard perturbation-based approach of Abernethy et al. (2008) in the context of unconstrained Bandit Linear Optimization (uBLO). We show the surprising result that in the unconstrained setting, this approach effectively reduces Bandit Linear Optimization (BLO) to a standard Online Linear Optimization (OLO) problem. Our framework improves on prior work in several ways. First, we derive expected-regret guarantees when our perturbation scheme is combined with comparator-adaptive OLO algorithms, leading to new insights about the impact of different adversarial models on the resulting comparator-adaptive rates. We also extend our analysis to dynamic regret, obtaining the optimal $\sqrt{P_T}$ path-length dependencies without prior knowledge of $P_T$. We then develop the first high-probability guarantees for both static and dynamic regret in uBLO. Finally, we discuss lower bounds on the static regret, and prove the folklore $Ω(\sqrt{dT})$ rate for adversarial linear bandits on the unit Euclidean ball, which is of independent interest.

We study dynamic regret minimization in unconstrained adversarial linear bandit problems. In this setting, a learner must minimize the cumulative loss relative to an arbitrary sequence of comparators $\boldsymbol{u}_1,\ldots,\boldsymbol{u}_T$ in $\mathbb{R}^d$, but receives only point-evaluation feedback on each round. We provide a simple approach to combining the guarantees of several bandit algorithms, allowing us to optimally adapt to the number of switches $S_T = \sum_t\mathbb{I}\{\boldsymbol{u}_t \neq \boldsymbol{u}_{t-1}\}$ of an arbitrary comparator sequence. In particular, we provide the first algorithm for linear bandits achieving the optimal regret guarantee of order $\mathcal{O}\big(\sqrt{d(1+S_T) T}\big)$ up to poly-logarithmic terms without prior knowledge of $S_T$, thus resolving a long-standing open problem.

We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \emph{unknown} intervention targets.