# AOS4 - A2021: Robust MAVT tutorial * Performance table |Alternative | Dimension 1 | Dimension 2 | Dimension 3| |---|---|---|---| | $x_1$ | 10 | 50 | 70 | | $x_2$ | 34 | 56 | 84 | | $x_3$ | 40 | 90 | 45 | | $x_4$ | 30 | 10 | 70 | | $x_5$ | 60 | 80 | 45 | | $x_6$ | 49 | 56 | 54 | | $x_7$ | 84 | 12 | 45 | | $x_8$ | 20 | 40 | 78 | | $x_9$ | 50 | 80 | 30 | | $x_{10}$| 12 | 98 | 12 | | $x_{11}$| 39 | 65 | 50 | |$x_{12}$| 10 | 78 | 32 | * Preference model: Weighted Sum... again! $g_w(x) = w_1.g_1(x) + w_2.g_2(x) + w_3.g_3(x)$ with $w_1 + w_2 + w_3 = 1$ et $w_i \ge 0$, $i \in\{ 1,2,3\}$. * Preference information: $PI = \{PI_1, PI_2, PI_3, PI_4\}$ $PI_1$: "$x_1$ is at least as attractive than $x_4$", $PI_2$: "$x_5$ is not worse than $x_3$, $PI_3$: "$x_2$ is at least as good as $x_6$", $PI_4$: "None of the three dimensions can contribute more than half the total score" * Questions 1. Draw the *parameter space* $(w_1, w_2)$ 2. In this parameter space, draw each constraint $PI_j, j \in\{ 1,2,3,4\}$ 3. Draw the line $x_5 \sim x_2$. Is $x_5$ necessarily/possibly/impossibly preferred to $x_2$? 4. Find the coordinates $w^\star_k$ of the vertices $A_k, k\in\{ 1,2,3,4,5\}$ of the polygon $\Omega_{PI}$ 5. Show that $x$ is necessarily preferred to $y$ iff $x$ is preferred to $y$ for all $w_k, k\in\{ 1,2,3,4,5\}$ 6. Write a program that takes as an input a list $X=[x_1,...,x_n]$ of performance vectors in $[0,100]^3$, a set of preference statements $PI \subset X^2$ and returns the binary relation over $X$ traducing necessary preference. It could rely on solving a LP with objective function $\max g_w(x) - g_w(y)$.
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Last mile explanations for the additive model

Comparison with other approaches Question: So what would be a PI-explanation/sufficient reasons in our context? Reminder: sufficient reasons justifying the classification, irrespective of the value of other criteria. Let us for instance the first example of the paper $s_1 = cdefg \succ ad = s_2$, giving vector $(-1,0,+1,0,+1,+1,+1)$. We get two explanations by means of sufficient reasons (easy to compute, cf. Marques-Silva et al.): $cef$ are satisfied by $s_1$ but not by $s_2$, given that $bd$ are equal, is a sufficient reasons (ie. given that $bd$ are equal, $cef$ is actually preferred to $ag$). Note that for instance $ceg$ would not be a sufficient reason. $cefg$ are satisfied by $s_1$ but not by $s_2$, given that $b$ is equal, is a sufficient reason (ie. given that $b$ is equal, $cefg$ is preferred to $ad$) How much information is revealed

1/20/2022
Explaining inductive derivations with transductive arguments

Key concept de nombreuses approches XAI sont locales (i.e. elles cherchent à éclairer une recommandation particulière), contrefactuelles (i.e. elles considèrent des mondes alternatifs où la question posée serait "ni tout à fait la même, ni tout à fait une autre") de fait, ces approches sont de nature abductive (i.e. le processus décisionnel et son issue sont figés, et on cherche à spécifier les intrants - le candidat) par construction, une approche abductive fige le processus décisionnel, et ne permet pas sa remise en question Exemple typique : explications fondées sur les impliquants premiers (Marquis 2020, Darwiche ??, Marques-Silva 2020) - on identifie un sous ensemble minimal d'attributs du candidat tel que toute complétion conduise à la même recommandation Or, si on est amené à expliquer une recommandation, c'est qu'on postule la possibilité de la contester. Cette contestation peut porter sur les causes premières mises en avant par le dispositif explicatif, mais aussi, peut-être, sur les règles de dérivation qui permettent de relier les causes aux effets

1/20/2022
AOS4 - UTA: Learning a piecewise linear additive value model with LP

Description of the preference model A simple, yet effective, procedure for fitting a value model to the preference expressed by a decision maker has been proposed by Jacquet-Lagrèze & Siskos (1982) MAVT: the analyst assumes a linear model of the preference of the Decision maker $$V(x) = \sum_i v_i(x_i)\ \text{with}\ v_i : \mathcal X_i \to \mathbb [0, w_i], \sum_i w_i = 1$$ Parametrized value functions: the marginal value functions are assumed to be piecewise linear, with predefined cutting points $x_i^1 < ...< x_i^{k_i} \in \mathbb{X}_i$ Preference Information: the DM submits pairwise comparison statements of the form $a^j \succeq a^{j'}$ for some alternatives $a^j$ and $a^{j'}$ Computation: the representation that corresponds "best" to this stance is computed via linear programming Extensions: sorting (UTADIS), robust decision making (GRIP), using another parametric family of value functions...

12/14/2021
AOS4 - Assignment # 3

A bird-watching aficionado is looking to acquire a new camera. From his favorite guide, she gets information about devices in her price range: Model a b c d $g_1$ (Picture quality) 25

12/1/2021
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