A method for concept-based learning using probabilistic inference and expert rules.
problem Concept-based learning with limited training data.
method Divide images into patches, transform into embeddings, cluster, and use frequentist inference to find concepts.
result FI-CBL outperforms concept bottleneck model in small data scenarios.
CAVs reveal latent concept distributions, but are vulnerable to adversarial attacks.
problem Understanding latent concept encodings in AI models.
method Probabilistic perspective on CAVs, deriving mean and covariance.
result CAVs can be adversarially manipulated, highlighting a vulnerability.
Counterfactual fairness not equivalent to demographic parity, finds study.
problem Equivalence between causal and probabilistic concepts in fairness metrics.
method Close examination of recent claim about counterfactual fairness.
result Counterfactual fairness is not equivalent to demographic parity.
Extends partitioned local depth concept with probabilistic considerations.
problem Uncertain, variable, and conflicting information in data.
method Partitioned local depth with probabilistic concepts of local relevance and support division.
result Extends original ideas to handle uncertain data.
This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in f…
Generative concept representations have three major advantages over discriminative ones: they can represent uncertainty, they support integration of learning and reasoning, and they are good for unsupervised and semi-supervised learning. We discuss probabilistic and generative deep learning, which generative concept re…
This paper introduces a probabilistic framework for k-shot image classification. The goal is to generalise from an initial large-scale classification task to a separate task comprising new classes and small numbers of examples. The new approach not only leverages the feature-based representation learned by a neural net…
The paper studies the concepts of hedging and arbitrage in a non probabilistic framework. It provides conditions for non probabilistic arbitrage based on the topological structure of the trajectory space and makes connections with the usual notion of arbitrage. Several examples illustrate the non probabilistic arbitrag…
Proposes PRMs for interpreting financial risk concept drift.
problem Concept drift in high-stakes predictions like credit risk.
method Probabilistic Rule Models (PRMs) using Markov Logic Networks.
result Interpretable rules explain borrower risk changes.
Unified framework for testing deep learning models with concept activation vectors.
problem Statistical instability and discontinuity in testing with concept activation vectors.
method Introducing α-TCAV, a generalized framework that replaces the indicator function with a parameterized smooth function.
result Unified probabilistic formulation that subsumes TCAV and Multi-TCAV, providing principled guidance on tuning the parameter.
Embedding methods which enforce a partial order or lattice structure over the concept space, such as Order Embeddings (OE) (Vendrov et al., 2016), are a natural way to model transitive relational data (e.g. entailment graphs). However, OE learns a deterministic knowledge base, limiting expressiveness of queries and the…
New approach uses neural networks to learn program structure and parameters.
problem Learning programs and their structure efficiently.
method Free category prior over programs, end-to-end learning of structure and parameters.
result Neural networks can serve as primitives in probabilistic programs.
New framework uses conformal predictions for robust, scalable machine learning classification.
problem Developing robust and reliable machine learning models for classification.
method Introducing scalable classifiers linked to statistical order theory and probabilistic learning theory, defining a score function and conformal safety set.
result Demonstrated practical implications in cybersecurity for identifying DNS tunneling attacks.
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate probabilistic inference were feasible, and (ii) small or medium-sized data sets which fit …
Generative Neuro-Symbolic model learns from raw data with rich conceptual representations.
problem Learning rich, general-purpose conceptual representations from raw perceptual inputs.
method Generative Neuro-Symbolic (GNS) model combining symbolic and neural network approaches.
result Model learns from raw data and generalizes to 4 unique tasks.
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but requires only basic algebra and probability theory to understand and verify. Th…
Recent advances in machine learning for medical imaging have led to impressive increases in model complexity and overall capabilities. However, the ability to discern the precise information a machine learning method is using to make decisions has lagged behind and it is often unclear how these performances are in fact…
Calibrating classifiers reduces grouping loss using sufficiency criteria.
problem Grouping loss in probabilistic classifier calibration is often overlooked.
method Revisited Langford & Zadrozny's probing reduction approach and introduced Brier curves.
result The probing reduction approach reduces grouping loss and supports sufficient calibration.
ECBMs unify concept-based interpretations in deep learning models.
problem Suboptimal final accuracy and lack of concept interaction and conditional dependencies.
method ECBMs use a set of neural networks to define joint energy, enabling concept correction and conditional dependency quantification.
result ECBMs achieve higher accuracy and richer concept interpretations compared to state-of-the-art methods.
PACE explains ViTs by modeling patch-level concept distributions, surpassing existing methods.
problem Lack of trustworthy post-hoc explanations for Vision Transformers (ViTs)
method Variational Bayesian explanation framework (PACE)
result PACE surpasses state-of-the-art methods in meeting desiderata for ViT explanations.
Non-convex optimization problems often arise from probabilistic modeling, such as estimation of posterior distributions. Non-convexity makes the problems intractable, and poses various obstacles for us to design efficient algorithms. In this work, we attack non-convexity by first introducing the concept of \emph{probab…
New DKPP family controls positive and negative dependence in random subsets.
problem Challenges in seamlessly bridging probabilistic models for positive and negative dependence.
method Introduced DKPP family and developed computational methods for probabilistic operations and inference.
result Controllability of positive and negative dependence demonstrated through numerical experiments.
Develops probabilistic safety regions for scalable classifiers.
problem Minimizing misclassification errors in supervised classification.
method Introduces probabilistic safety regions and scalable classifiers.
result Probabilistic certifications for classifier performance.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called…
The paper studies batch decompositions of random datasets with probabilistic similarity constraints.
problem Understanding how to optimally split large datasets into batches for better model learning.
method Assumes independent data points from a space, defines similarity, and uses probabilistic and martingale methods to find bounds on batch sizes.
result Demonstrates an inherent tradeoff between relaxing similarity constraints and batch size, and provides bounds for maximum similarity subsets.
Hybrid model learns novel handwritten characters better than neural or symbolic models alone.
problem Generating novel yet structured concepts.
method Neuro-symbolic model combining neural networks and probabilistic programs.
result Hybrid model outperforms alternative models in learning and generalizing novel handwritten characters.
Normal-bundle bootstrap generates new data preserving geometric structure.
problem Probabilistic models often exhibit salient geometric structure.
method NBB method decomposes probability measure into manifold and normal spaces, estimates manifold as density ridge, and generates new data by bootstrapping projection vectors.
result NBB generates new data that preserves the geometric structure of a given data set.
Study particle dynamics in non-differentiable fractal spaces.
problem Understanding motion in non-smooth, probabilistic geometries.
method Use fiber bundle theory to characterize multivalued geodesic trajectories.
result Developed a hybrid theory combining surface and stochastic process theories.
New concept of partial law invariance connects decision theory and financial risk management.
problem Connecting decision theory and financial risk management under uncertainty.
method Characterizing partially law-invariant coherent risk measures via a novel representation formula.
result Strong partial law invariance bridges the gap between existing risk measure representations.
This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces fundamental concepts and algorithms by building on first principles, while also e…
The paper reviews and extends calibration concepts for classification and regression.
problem Formalizing compatibility between probabilistic predictions and outcomes.
method Review and extension of existing calibration concepts, introduction of new concepts.
result Hierarchical relations between calibration concepts for various data types.
A framework monitors and diagnoses concept drift in supervised learning models.
problem Changes in predictive relationships over time render models suboptimal.
method Score vector monitoring using exponentially weighted moving average.
result Score-based approach detects concept drift more effectively than error-based methods.
Hybrid framework combines PGMs and TNs for complex probabilistic modeling.
problem Combining quantum-like correlations into PGM models.
method Introducing decoherence to convert probabilistic TN models into PGMs.
result Hybrid models can represent and combine strengths of both PGMs and TNs.
Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.
problem Uncertainty in neural network weights is hard to specify and interpret.
method Integrates probabilistic layers with standard deterministic layers for function uncertainty.
result Improves probabilistic inference by encoding function uncertainty.
Neurosymbolic predictors fail to model uncertainty under independence assumption.
problem Neurosymbolic predictors' reliance on independence assumption limits their ability to model uncertainty.
method Formal analysis of NeSy predictors under independence assumption.
result Assuming independence among symbolic concepts prevents NeSy predictors from representing uncertainty.
Global physical event detection has traditionally relied on dense coverage of physical sensors around the world; while this is an expensive undertaking, there have not been alternatives until recently. The ubiquity of social networks and human sensors in the field provides a tremendous amount of real-time, live data ab…
Simplifies efficient estimation via automatic differentiation and probabilistic programming.
problem Constructing efficient estimators for complex statistical models.
method Automatic differentiation applied to statistical functionals, avoiding the need to derive efficient influence functions.
result Users can generate efficient estimators with minimal code, simplifying the process for non-experts.
Sequence models quantify uncertainty over latent concepts.
problem Quantifying uncertainty in latent environments.
method Exchangeable sequence models, equivalent to empirical Bayes and posterior inference.
result Sequence prediction loss controls uncertainty quantification.
A new method in finance without probabilities or integrals.
problem Creating a model-free approach to continuous-time finance.
method Pathwise approach using causal functional calculus and transition principle of Isaacs.
result A fully non-linear path-dependent equation characterizes optimal solutions.
Prb-GAN uses dropout and variational inference to improve GAN performance.
problem GANs struggle with mode loss and training instability.
method Introduces Prb-GANs with dropout and variational inference for parameter distribution.
result Improves GAN performance through dropout and variational inference.
Word embeddings have demonstrated strong performance on NLP tasks. However, lack of interpretability and the unsupervised nature of word embeddings have limited their use within computational social science and digital humanities. We propose the use of informative priors to create interpretable and domain-informed dime…
This review covers predictive uncertainty estimation in machine learning.
problem Improving the communication of uncertainty in machine learning predictions.
method A comprehensive review of probabilistic prediction methods from early statistical models to recent machine learning algorithms.
result The review highlights the importance of consistent scoring functions and proper scoring rules for assessing probabilistic predictions.
COLEP improves robustness of conformal prediction via probabilistic circuits.
problem Adversarial perturbations can undermine the coverage guarantees of conformal prediction.
method COLEP uses probabilistic circuits to learn and reason about different semantic concepts, providing certifiable coverage guarantees.
result COLEP achieves higher prediction coverage and accuracy than a single model, especially with non-trivial knowledge models.
This paper uses SLT to ensure learning guarantees in CD detection.
problem Lack of learning guarantees in CD detection algorithms.
method Adapting SLT assumptions to CD scenarios to ensure learning guarantees.
result Ensured learning guarantees in CD detection algorithms.
It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is based in large part on the unifying concept of tensors, we describe a software a…
Kernel density matrices simplify probabilistic deep learning.
problem Representing joint probability distributions of continuous and discrete variables.
method Extending density matrices to a reproducing kernel Hilbert space.
result Versatile representation for marginal and joint probability distributions.
Stochastic computation graphs (SCGs) provide a formalism to represent structured optimization problems arising in artificial intelligence, including supervised, unsupervised, and reinforcement learning. Previous work has shown that an unbiased estimator of the gradient of the expected loss of SCGs can be derived from a…
Causal discovery algorithms can help generate legal arguments.
problem Leveraging causal discovery algorithms in legal decision-making.
method Prepared a legal dataset, annotated with 17 legal concepts, applied causal discovery algorithms, and quantified degrees of belief.
result Some causal relationships help generate viable legal arguments.