We develop a method that addresses the problem of causality for multivariate time series with few assumptions. It consists of Causality defines the relationship between cause and effect. In multivariate merging a causal discovery algorithm, the PC algorithm [6], with an time series field, this notion allows to characterize the information theoretic-based causal inference measure, the Partial links between several time series considering temporal lags. These Mutual Information from Mixed Embedding [7] (PMIME). Based on phenomena are particularly important in medicine to analyze the information theory, the PMIME allows to limit assumptions on the effect of a drug for example, in manufacturing to detect the causes data but also on the links between time series. With this measure, of an anomaly in a complex system or in social sciences... Most of the PC algorithm gives causal relationships among multivariate the time, studying these complex systems is made through correlation time series, by representing the causality with a Directed Acyclic only. But correlation can lead to spurious relationships.

Interpretable machine learning seeks to understand the reasoning process of complex black-box systems that are long notorious for lack of explainability. One flourishing approach is through counterfactual explanations, which provide suggestions on what a user can do to alter an outcome. Not only must a counterfactual example counter the original prediction from the black-box classifier but it should also satisfy various constraints for practical applications. Diversity is one of the critical constraints that however remains less discussed. While diverse counterfactuals are ideal, it is computationally challenging to simultaneously address some other constraints. Furthermore, there is a growing privacy concern over the released counterfactual data. To this end, we propose a feature-based learning framework that effectively handles the counterfactual constraints and contributes itself to the limited pool of private explanation models. We demonstrate the flexibility and effectiveness of our method in generating diverse counterfactuals of actionability and plausibility. Our counterfactual engine is more efficient than counterparts of the same capacity while yielding the lowest re-identification risks.

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projection variables, where multiple solutions that are identical when restricted to the projection variables count as only one solution. Inspired by the observation that the so-called "treewidth" is one of the most prominent structural parameters, our algorithm utilizes small treewidth of the primal graph of the input instance. More precisely, it runs in time O(2^2k+4n2) where k is the treewidth and n is the input size of the instance. In other words, we obtain that the problem PMC is fixed-parameter tractable when parameterized by treewidth. Further, we take the exponential time hypothesis (ETH) into consideration and establish lower bounds of bounded treewidth algorithms for PMC, yielding asymptotically tight runtime bounds of our algorithm. While the algorithm above serves as a first theoretical upper bound and although it might be quite appealing for small values of k, unsurprisingly a naive implementation adhering to this runtime bound suffers already from instances of relatively small width. Therefore, we turn our attention to several measures in order to resolve this issue towards exploiting treewidth in practice: We present a technique called nested dynamic programming, where different levels of abstractions of the primal graph are used to (recursively) compute and refine tree decompositions of a given instance. Finally, we provide a nested dynamic programming algorithm and an implementation that relies on database technology for PMC and a prominent special case of PMC, namely model counting (#Sat). Experiments indicate that the advancements are promising, allowing us to solve instances of treewidth upper bounds beyond 200.

Valued constraint satisfaction problems with ordered variables (VCSPO) are a special case of Valued CSPs in which variables are totally ordered and soft constraints are imposed on tuples of variables that do not violate the order. We study a restriction of VCSPO, in which soft constraints are imposed on a segment of adjacent variables and a constraint language $\Gamma$ consists of $\{0,1\}$-valued characteristic functions of predicates. This kind of potentials generalizes the so-called pattern-based potentials, which were applied in many tasks of structured prediction. For a constraint language $\Gamma$ we introduce a closure operator, $ \overline{\Gamma^{\cap}}\supseteq \Gamma$, and give examples of constraint languages for which $|\overline{\Gamma^{\cap}}|$ is small. If all predicates in $\Gamma$ are cartesian products, we show that the minimization of a generalized pattern-based potential (or, the computation of its partition function) can be made in ${\mathcal O}(|V|\cdot |D|^2 \cdot |\overline{\Gamma^{\cap}}|^2 )$ time, where $V$ is a set of variables, $D$ is a domain set. If, additionally, only non-positive weights of constraints are allowed, the complexity of the minimization task drops to ${\mathcal O}(|V|\cdot |\overline{\Gamma^{\cap}}| \cdot |D| \cdot \max_{\rho\in \Gamma}\|\rho\|^2 )$ where $\|\rho\|$ is the arity of $\rho\in \Gamma$. For a general language $\Gamma$ and non-positive weights, the minimization task can be carried out in ${\mathcal O}(|V|\cdot |\overline{\Gamma^{\cap}}|^2)$ time. We argue that in many natural cases $\overline{\Gamma^{\cap}}$ is of moderate size, though in the worst case $|\overline{\Gamma^{\cap}}|$ can blow up and depend exponentially on $\max_{\rho\in \Gamma}\|\rho\|$.

Making Smart Cities more sustainable, resilient and democratic is emerging as an endeavor of satisfying hard constraints, for instance meeting net-zero targets. Decentralized multi-agent methods for socio-technical optimization of large-scale complex infrastructures such as energy and transport networks are scalable and more privacy-preserving by design. However, they mainly focus on satisfying soft constraints to remain cost-effective. This paper introduces a new model for decentralized hard constraint satisfaction in discrete-choice combinatorial optimization problems. The model solves the cold start problem of partial information for coordination during initialization that can violate hard constraints. It also preserves a low-cost satisfaction of hard constraints in subsequent coordinated choices during which soft constraints optimization is performed. Strikingly, experimental results in real-world Smart City application scenarios demonstrate the required behavioral shift to preserve optimality when hard constraints are satisfied. These findings are significant for policymakers, system operators, designers and architects to create the missing social capital of running cities in more viable trajectories.

In this paper we consider the problem of deciding if a (likely incomplete) description of a system of events is consistent, the network consistency problem for the point algebra of partially ordered time (POT). This is achieved by a sophisticated enumeration of structures similar to total orders, which are then greedily expanded towards a solution. While similar ideas have been explored earlier for related problems it turns out that the analysis for POT is non-trivial and requires significant new ideas. Qualitative reasoning is an important formalism in artificial intelligence where the objective is to reason about continuous properties given certain relations between the unknown entities. Two important subfields are temporal reasoning, e.g., the point algebra for partially ordered time (POT), Allen's interval algebra (A), and the point algebra for branching time, and spatial reasoning, e.g., the region connection calculus (RCC), the cardinal direction calculus, and the rectangle algebra.

We study online learning problems in which a decision maker has to make a sequence of costly decisions, with the goal of maximizing their expected reward while adhering to budget and return-on-investment (ROI) constraints. Previous work requires the decision maker to know beforehand some specific parameters related to the degree of strict feasibility of the offline problem. Moreover, when inputs are adversarial, it requires the existence of a strictly feasible solution to the offline optimization problem at each round. Both requirements are unrealistic for practical applications such as bidding in online ad auctions. We propose a best-of-both-worlds primal-dual framework which circumvents both assumptions by exploiting the notion of interval regret, providing guarantees under both stochastic and adversarial inputs. Our proof techniques can be applied to both input models with minimal modifications, thereby providing a unified perspective on the two problems. Finally, we show how to instantiate the framework to optimally bid in various mechanisms of practical relevance, such as first- and second-price auctions.

Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of NP-hard reasoning tasks, improving the running time from the naive $2^{O(n^2)}$ to $O^*((1.0615n)^{n})$, with even faster algorithms for unit intervals a bounded number of overlapping intervals (the $O^*(\cdot)$ notation suppresses polynomial factors). Despite these improvements the best known lower bound is still only $2^{o(n)}$ (under the exponential-time hypothesis) and major improvements in either direction seemingly require fundamental advances in computational complexity. In this paper we propose a novel framework for solving NP-hard qualitative reasoning problems which we refer to as dynamic programming with sublinear partitioning. Using this technique we obtain a major improvement of $O^*((\frac{cn}{\log{n}})^{n})$ for Allen's interval algebra. To demonstrate that the technique is applicable to more domains we apply it to a problem in qualitative spatial reasoning, the cardinal direction point algebra, and solve it in $O^*((\frac{cn}{\log{n}})^{2n/3})$ time. Hence, not only do we significantly advance the state-of-the-art for NP-hard qualitative reasoning problems, but obtain a novel algorithmic technique that is likely applicable to many problems where $2^{O(n)}$ time algorithms are unlikely.

In executable task-oriented semantic parsing, the system aims to translate users' utterances in natural language to machine-interpretable programs (API calls) that can be executed according to pre-defined API specifications. With the popularity of Large Language Models (LLMs), in-context learning offers a strong baseline for such scenarios, especially in data-limited regimes. However, LLMs are known to hallucinate and therefore pose a formidable challenge in constraining generated content. Thus, it remains uncertain if LLMs can effectively perform task-oriented utterance-to-API generation where respecting API's structural and task-specific constraints is crucial. In this work, we seek to measure, analyze and mitigate such constraints violations. First, we identify the categories of various constraints in obtaining API-semantics from task-oriented utterances, and define fine-grained metrics that complement traditional ones. Second, we leverage these metrics to conduct a detailed error analysis of constraints violations seen in state-of-the-art LLMs, which motivates us to investigate two mitigation strategies: Semantic-Retrieval of Demonstrations (SRD) and API-aware Constrained Decoding (API-CD). Our experiments show that these strategies are effective at reducing constraints violations and improving the quality of the generated API calls, but require careful consideration given their implementation complexity and latency.

Mixed integer problems are ubiquitous in decision making, from discrete device settings and design parameters, unit production, and on/off or yes/no decision in switches, routing, and social networks. Despite their prevalence, classical optimization approaches for combinatorial optimization remain prohibitively slow for fast and accurate decision making in dynamic and safety-critical environments with hard constraints. To address this gap, we propose SiPhyR (pronounced: cipher), a physics-informed machine learning framework for end-to-end learning to optimize for combinatorial problems. SiPhyR employs a novel physics-informed rounding approach to tackle the challenge of combinatorial optimization within a differentiable framework that has certified satisfiability of safety-critical constraints. We demonstrate the effectiveness of SiPhyR on an emerging paradigm for clean energy systems: dynamic reconfiguration, where the topology of the electric grid and power flow are optimized so as to maintain a safe and reliable power grid in the presence of intermittent renewable generation. Offline training of the unsupervised framework on representative load and generation data makes dynamic decision making via the online application of Grid-SiPhyR computationally feasible.