Inverse problems are among the most challenging in computational and applied science and have been studied extensively (Bunge, 2006; Hensel, 1991; Kaipio & Somersalo, 2004; Kirsch, 1996; Pizlo, 2001; Sabatier, 2000; Tarantola, 2005; Woodbury, 2002). Although there is no precise definition, the term refers to a wide range of problems that are generally described by saying that their answer is known, but not the question. An obvious example would be “Guessing the intentions of a person from her/his behavior.” In our case: “Guessing a past event from its vestiges.” In archaeology, the main source for inverse problems lies in the fact that archaeologists generally do not know why archaeological observables have the shape, size, texture, composition, and spatiotemporal location they have. Instead, we have sparse and noisy observations or measurements of perceptual properties, and an incomplete knowledge of relational contexts and possible causal processes. From this information, an inverse engineering approach should be used to interpret adequately archaeological observables as the material consequence of some social actions.
TopInverse Reasoning
Inverse problems are among the most challenging in computational and applied science and have been studied extensively (Bunge, 2006; Hensel, 1991; Kaipio & Somersalo, 2004; Kirsch, 1996; Pizlo, 2001; Sabatier, 2000; Tarantola, 2005; Woodbury, 2002). Although there is no precise definition, the term refers to a wide range of problems that are generally described by saying that their answer is known, but not the question. An obvious example would be “Guessing the intentions of a person from her/his behavior.” In our case: “Guessing a past event from its vestiges.” In archaeology, the main source for inverse problems lies in the fact that archaeologists generally do not know why archaeological observables have the shape, size, texture, composition, and spatiotemporal location they have. Instead, we have sparse and noisy observations or measurements of perceptual properties, and an incomplete knowledge of relational contexts and possible causal processes. From this information, an inverse engineering approach should be used to interpret adequately archaeological observables as the material consequence of some social actions.
A naïve solution would be to list all possible consequences of the same cause. This universal knowledge base would contain all the knowledge needed to “guess” in a rational way the most probable cause of newly observed effects. This way of solving inverse problems implies a kind of instance-based learning, which represents knowledge in terms of specific cases or experiences and relies on flexible matching methods to retrieve these cases and apply them to new situations. This way of learning, usually called case-based learning, is claimed to be a paradigm of the human way of solving complex diagnostic problems in domains like archaeology. To act as a human expert, a computer system needs to make decisions based on its accumulated experience contained in successfully solved cases. Descriptions of past experiences, represented as cases, are stored in a knowledge base for later retrieval. When the computer sensor perceives a new case with similar parameters, the system searches for stored cases with problem characteristics similar to the new one, finds the closest fit, and applies the solutions of the old case to the new case. Successful solutions are tagged to the new case and both are stored together with the other cases in the knowledge base. Unsuccessful solutions also are appended to the case base along with explanations as to why the solutions did not work.
The suggestion that the intelligent machine should define causal events in terms of the observation of a repeated series of similar events typically relies on a kind of regularity assumption demanding that ‘similar problems have similar solutions’ (Hüllermeier, 2007; Kolodner, 1993). In other words, a learning machine can be broadly defined as any device whose actions are influenced by past experiences, so that learning procedures changes within an agent that over time enable it to perform more effectively within its environment (Arkin, 1998). The idea is that once a system has a rule that fits past data, if the future is similar to the past, the system will make correct predictions for novel instances (Alpaydin, 2004). This mechanism implies the search for maximal explanatory similarity between the situation being explained and some previously explained scenario (Falkenheimer, 1990).