Related papers: Pearl's and Jeffrey's Update as Modes of Learning …
Learning a sequence of tasks without access to i.i.d. observations is a widely studied form of continual learning (CL) that remains challenging. In principle, Bayesian learning directly applies to this setting, since recursive and one-off…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
The Josephus problem is a well--studied elimination problem consisting in determining the position of the survivor after repeated applications of a deterministic rule removing one person at a time from a given group. A natural probabilistic…
Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
Suppose we have $n$ different types of self-replicating entity, with the population $P_i$ of the $i$th type changing at a rate equal to $P_i$ times the fitness $f_i$ of that type. Suppose the fitness $f_i$ is any continuous function of all…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
This paper investigates a novel nonlinear update rule based on temporal difference (TD) errors in reinforcement learning (RL). The update rule in the standard RL states that the TD error is linearly proportional to the degree of updates,…
The causal (belief) network is a well-known graphical structure for representing independencies in a joint probability distribution. The exact methods and the approximation methods, which perform probabilistic inference in causal networks,…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Theory of Probability is distinguished by several high-level philosophical attitudes, some stressed by Jeffreys, some implicit. By reviewing these we may recognize the importance in this work in the historical development of statistics.…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…
Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due…
We consider an information updating system where a source produces updates as requested by a transmitter. The transmitter further processes these updates in order to generate $partial$ $updates$, which have smaller information compared to…
We derive the Jeffreys prior for the parameter of the Multivariate Ewens Distribution and study some of its properties. In particular, we show that this prior is proper and has no finite moments. We also investigate the impact of this…